If you want to get to the heart of the truly dysfunctional relationship between Yahoo and Microsoft, consider the alleged 24-hour deadline that Yahoo claimed Microsoft and its loyal sidekick, activist investor Carl Icahn, gave the company to respond to the pair’s most recent joint proposal to settle their differences.

I say “alleged,” because as in all things related to this takeover mess, the trio disagrees on exactly what even that meant.

Frankly, it’s enough to make one think former President Bill Clinton’s definition of what “is” is makes more sense.

Yahoo (YHOO), in a rather strong statement Saturday night, said Microsoft tried to jam the company into swallowing a semi-sweetened new search deal with a side order of Icahn control.

But Microsoft (MSFT) sources scoff at the notion, noting that they only wanted to try to move a deal forward more quickly than the previous interminable roundelays that have exhausted everyone.

Before we get to this latest disagreement, here are the terms of the new Microsoft/Icahn joint deal to take control of Yahoo’s search business and hand over the rest to Icahn, which, according to numerous sources from both sides, was quickly rejected by Yahoo Saturday.

The deal included:

– $1 billion for Yahoo’s search business and a five-year guarantee of $2.3 billion in search ad revenue, with an option to renew it for another five years at a $1.6 billion minimum;

– An offer by Microsoft to buy $3.9 billion of Yahoo shares, and lend the company $2.8 billion at a five percent interest rate, by taking over a part of its debt. The money would be used to give a special dividend to shareholders;

– An agreement to raise the TAC rate (a payout to Yahoo on each search query) to 85 percent from its former offer of 70 percent, for three years, and to 75 percent after that;

– A plan, unclear as to specifics, to spin off Yahoo’s Asian assets, with money going to shareholders;

– And, last of all and the obvious dealbreaker, Icahn would get control of the rest of the company, which includes the massive content and communications assets. Apparently, one or two current Yahoo board members could possibly stay on. Presumably, Icahn could then strike a deal to merge those with assets of News Corp.’s (NWS) MySpace or Time Warner’s (TWX) AOL. (News Corp. is the owner of Dow Jones and of this site.)

But, Yahoo rejected the proposal in strong terms, especially stressing that it would not negotiate such a big deal under a time constraint.

Here’s Yahoo’s official version, from a statement :

“The proposal was made on Friday evening and Yahoo! was given less than 24 hours to accept the proposal, the fundamental terms of which Microsoft and Mr. Icahn made clear they were unwilling to negotiate.”

And Chairman Roy Bostock piled on: “After negotiating among themselves without the involvement of Yahoo!, Carl Icahn and Microsoft presented us with a ‘take it or leave it’ proposal under which we would be required to restructure the Company, hand over to Microsoft Yahoo!’s valuable search business and to Carl Icahn the rest of the Company, giving us less than 24 hours to respond. It is ludicrous to think that our Board could accept such a proposal.”

Microsoft sources consider the talks much less dramatic that that, noting that Yahoo had been talking to Icahn all week, and especially Thursday, about a new deal to take over Yahoo’s search business, and that an Icahn board was mentioned.

And, they add, Bostock was the one who insisted to Icahn that he needed to talk to Microsoft CEO Steve Ballmer directly, even though the software giant had publicly said it was unwilling to do so anymore.

But several times, the trio, along with a passel of bankers and lawyers, did just this, starting last Thursday night and, most significantly, Friday afternoon for 45 minutes.

It was in that call that the three sides discussed the proposal in detail, which included slides sent from Microsoft, although there was no term sheet.

Ballmer, a source close to both Yahoo and Microsoft said, did express being tired of the endless loop Yahoo and Microsoft were caught in and said that he did not want prolonged negotiations to go on.

This was not an ultimatum, according to Microsoft sources, but more of an expression of weariness at a new round of tedious back-and-forth.

“This has just gotten impossible,” said one Microsoft source. “We just wanted to have talks that went somewhere.”

When pressed, some sources close to Yahoo do confirm that they talked extensively to Icahn and then Microsoft. The 24-hour number came about because Ballmer asked Bostock to get back to him the next day, but that it was not exactly what one would call a threat.

“We felt he was saying Microsoft was not willing to put more on the table and, if we agreed to it, it would have been on their terms,” one source explained.

You get the picture–this is how wars start.

And that’s where Yahoo is now headed with Icahn–and by extension, Microsoft–as their proxy fight shifts into high gear heading into Yahoo’s annual meeting on Aug. 1.

What would it take to get Yahoo and Microsoft to come to some sort of rational agreement to strike a partnership of some sort before that?

Well, Sigmund Freud might be a start–or even Dr. Phil at this point–in this warped relationship.

Now, it seems, we’ll be moving directly to Judge Judy.

More on that later today.

Called “The Comeback Id” (oh, how pun-ny!), the article has gotten a lot of attention for pointing out the rampant speculation that Clinton’s well-known penchant for marital infidelity had returned.

And the reason for that disturbing development, besides Clinton himself? The piece actually placed a good bit of the blame on Clinton’s close friend, grocery magnate and billionaire Ron Burkle (pictured here), who also has been one of the key directors at Yahoo (YHOO) in its takeover fight with Microsoft (MSFT).

It’s a wonder Burkle can focus on the turmoil at Yahoo, given how busy he appears to be in the article corrupting Clinton both personally and–worse–professionally, via some questionable investments the pair had made through Burkle’s Yucaipa Companies.

Writer Todd Purdum paints a decidedly unattractive picture of Burkle, noting even the tasteless nickname of Burkle’s plane these days, in a portrayal so rough that Yahoo CEO Jerry Yang’s tough treatment by the press recently looks like a walk in the park.

Well, almost.

In what amounts to a rant by Carl Icahn (pictured here), The Wall Street Journal gives the billionaire investor lots of room to kvetch about what he thinks of Yang, including asserting that he will oust the Yahoo founder if he wins his proxy fight against the company.

“I am amazed at the lengths that Jerry Yang and the board went to entrench themselves in this situation,” said Icahn.

Apparently, Icahn was the only one who didn’t get the memo that Yahoo has been consistently obstreperous about Microsoft’s many overtures, since–well, let’s do the exact calculations–forever. And a day.

Still, Icahn perseveres and hangs this old entrenched management chestnut on a lawsuit that was recently filed by shareholders that points to the massive and costly severance plan Yahoo sneakily put into place as a ploy to fend off Microsoft.

“It’s no longer a mystery to me why Microsoft’s offer isn’t around,” Icahn said. “How can Yahoo keep saying they’re willing to negotiate and sell the company on the one hand, while at the same time they’re completely sabotaging the process without telling anyone.”

How? By Yang opening his mouth, that’s how, and then doing nothing much.

As a student of this lugubrious style of Olympic dithering, I would point Icahn to Yang’s 100-day Sacred Cow VisionQuest, well before this soap opera got started.

You need to catch up pronto, Carl!

And speaking of people irked by Yang of late, investor Gordon Crawford (pictured here) also made some news yesterday with his investment in Veoh Networks, part of a $30 million round that included Intel Capital and Adobe Systems (ADBE).

Existing investors in the not-YouTube video service–Shelter Capital, Spark Capital, Goldman Sachs (GS), Michael Eisner’s Tornante Company, Time Warner Investments (TWX) and Jonathan Dolgen–also ponied up more money.

Crawford, the SVP of Capital Research Global Investors, manages a massive portfolio, and it is one of Yahoo’s biggest shareholders.

And, unlike Veoh, Yahoo is an investment Crawford has not been happy with recently.

“I am extremely angry at Jerry Yang and at the so-called independent board,” he said in an interview a month ago. “I’m hoping that there is such an outpouring of outrage that the board is embarrassed into revisiting this thing, but I’m not optimistic about that.”

And by independent board, by the way, he meant directors like–you guessed it–Ron Burkle!

At least Burkle’s not to blame for the so-so, lots-and-lots-missing–Google? What Google? (GOOG)–piece in the same Vanity Fair issue, an oral history of the Internet.

Called “How the Web Was Won,” it makes the founding of the world’s most important medium seem awfully dull.

I’d recommend instead–as any sentient being would–the cover story on Angelina Jolie, with this sharp quote from her: “In my father’s generation, the product was 80% of what you were putting into the world, and your personal life was 20%. It now seems that 80% of the product I put out is silly, made-up stories and what I’m wearing.”

Or not wearing, in the case of the pictures of Jolie in this article.