Talks between Yahoo and Microsoft have failed for the second time.

Yahoo said Thursday afternoon that Microsoft has refused to buy Yahoo for $33 a share, the price Microsoft offered May 3 and then pulled off the table when Yahoo’s co-founders held out for $37. Microsoft refusal makes its “strategic clarity” suspect.

Yahoo, in turn, refused to sell Microsoft just its search business, which Microsoft was willing to buy. No terms were disclosed but Microsoft claims Yahoo could have made a kiling.

With nothing left to talk about, all negotiations are off, Yahoo said, sending its shares reeling. They closed down 10% to $23.36 after being down 13% or ~$3.50 to $22.70, closer to where it was 19 weeks ago when Microsoft entered the scene. The stock has been artificially propped up ever since on speculation a deal would be cut.

Conversely Microsoft shares rose ~4% to $28.25, up $1.12 cents on the news that it wouldn’t have to spend all that money and cope with integrating an unfriendly and flagging prize.

With Microsoft apparently out of the picture – even if Microsoft in a prepared statement said it’s still willing to do a partial deal for more money than Yahoo can dream about this second – Yahoo stuck its head in the lion’s mouth and announced an advertising-search deal with Google, which seems on the face of it a horrific outcome for Microsoft, which reportedly offered $40 a share for Yahoo a year ago.

Of course any Yahoo-Google deal has to clear antitrust scrutiny and the waterhole poisoning of Microsoft lobbyists.

A Wall Street Journal blog observed that “Yahoo destroyed itself to save itself. Microsoft tried to get stronger, but only ended up exposing its own weakness. Somehow Google emerged triumphant, effectively neutralizing its two biggest competitors.

“That is what makes the Yahoo-Microsoft non-merger such a spectacular failure. Never have so few failed so many for so much at stake.”

In the statement Yahoo released Thursday it said discussions concluded after “numerous meetings and conversations with Microsoft regarding a number of transaction alternatives, including a meeting between Yahoo! and Microsoft on June 8th [Sunday] in which chairman Roy Bostock and other independent board members from Yahoo! participated. At that meeting, Microsoft representatives stated unequivocally that Microsoft is not interested in pursuing an acquisition of all of Yahoo!, even at the price range it had previously suggested.

“With respect to an acquisition of Yahoo!’s search business alone that Microsoft had proposed, Yahoo!’s board of directors has determined, after careful evaluation, that such a transaction would not be consistent with the company’s view of the converging search and display marketplaces, would leave the company without an independent search business that it views as critical to its strategic future and would not be in the best interests of Yahoo! stockholders.

“Yahoo! remains focused on maximizing value for stockholders by continuing to execute on its strategy of being the ‘starting point’ for the most consumers on the Internet and a ‘must buy’ for advertisers. The online advertising industry is projected to grow from $40 billion in 2007 to approximately $75 billion in 2010 and the company believes it has the right assets, strategic plan, board of directors and management team to capitalize on this growth opportunity.”

There has been no public reaction yet from billionaire corporate raider Carl Icahn – (the calm before the storm?); he wasn’t coming to the phone for anybody. Yesterday at least Icahn owned >4% of Yahoo and was embarked on a proxy fight to unseat the Yahoo board. He was banking on Microsoft buying the joint.

One would think that he’s going to want copies of the notes on the back and forth between Microsoft and Yahoo. And he’s going to want to plum the depths of Microsoft saying that it believes its alternative proposal for Yahoo “would have delivered in excess of $33 per share to the Yahoo shareholders.”

Microsoft’s full statement reads, “In the weeks since Microsoft withdrew its offer to acquire Yahoo!, the two companies have continued to discuss an alternative transaction that Microsoft believes would have delivered in excess of $33 per share to the Yahoo! shareholders. This partnership would ensure healthy competition in the marketplace, providing greater choice and innovation for advertisers, publishers and consumers.

“As stated on May 3rd and reiterated on May 18th Microsoft was not interested in rebidding for all of Yahoo!. Our alternative transaction remains available for discussion.”

Anyway, when last heard from Icahn wanted Yahoo “to stop dancing around” and publicly offer to sell out to Microsoft for $34.375 a share ($49.5 billion). And none of these penny ante half-way deals like selling them the search business like he’s been reading about in the paper. And if Microsoft didn’t bite then Yahoo should cut a search deal with Google – but nothing it can’t get out of in a heartbeat if Microsoft changes its mind. To which Yahoo basically replied, “You call THAT a plan? THAT’S not a plan,” although it sounds suspiciously like what’s going on. To which Icahn replied, “Oh, yeah, well, if your plans these last few years were so great how come you’re eating Google’s dust.”

Or, in his own words to Yahoo chairman Roy Bostock Monday: “Ironically, while you keep inquiring about my plans, it is interesting to note that Yahoo!’s board has been busy reaping great compensation benefits. Indeed, you made approximately $10,000 per week last year – not bad for a board member. I believe most of your shareholders would be interested in seeing your time sheets – especially in light of the fact that, in my estimation, most of your so-called ‘plans’ over the last few years have been failures. Remember the old adage – those who live in glass houses should not throw stones.”

And he added “While Google’s income from operations grew 59% per year for the last two years, Yahoo’s income from operations shrank 21%. What was the board doing over this period? Where was their great ‘plan’?”

Then they got down to the real taunting.

The argument of the week came down to the punitive, xenophobic, “change of control” employee severance plan with which Yahoo ringed itself like some kind of Bronze Age chevaux-de-frise to repel Microsoft’s advances.

According to Icahn, it was supposed to incentivize everybody at Yahoo to quit. It was also supposed to be what de-incentivized Microsoft – or at least moderated its sweetener. No one said any of this was taken off the table when Microsoft walked out again.

Last week – in his best line yet – Icahn called the severance plan a “self-destructive doomsday machine” straight out of James Bond.

Icahn calculates it could have added $2.4 billion to the cost of a takeover. Yahoo claimed it was more like $514 million or $845 million depending on whether 15% or 30% of Yahoo’s staff pulled the rip cord and resigned “for good reason” – like any change in responsibility, bonus opportunity or location.

In response, Yahoo claimed it was not, as Icahn characterizes it, a “poison pill” and yet it rang it like a leper’s bell warning that a successful Icahn proxy fight would trigger it.

Yahoo also says that its board can’t dismantle the plan, which it claims is a employee retention plan, until any possibility of change of control has been abandoned for 30 days; Icahn restarted the clock.

Icahn may be helped along by the pension funds suing Yahoo down in Delaware for malfeasance or whatever they call it, and which are now demanding an immediate jury trial – ahead of Yahoo’s stockholders meeting on August 1 – challenging the legality of the severance plan.

“A prompt trial on the validity of the severance plans is now essential and appropriate, not least because Yahoo’s board disabled itself from rescinding the severance plans during the pendency of a proxy fight, even if doing so is essential to realizing a favorable deal, and because Icahn’s slate is barred from rescinding the severance plans if it prevails in its proxy contest,” their lawyers argued.

The suit, which Yahoo is going to try to get quashed, along with any trial, already names co-founders Jerry Yang and David Filo and according to Reuters Icahn said during a speech at a New York Financial Writers Association dinner Tuesday that Yahoo’s board may be “personally liable” for sanctioning the plan.

Icahn also contended that Microsoft needs Yahoo to remain competitive during the next five years. It’s a “marriage made in heaven, even though they kind of hate each other,” Icahn said.

Yahoo Monday filed its proxy statement so it can go out and solicit votes to shoot down Icahn’s bid to unseat the board on August 1. It’s telling shareholders, “Even if you have previously signed a proxy card send by the Icahn Entities, you have the right to change your vote. Only the latest dated proxy you submit will be counted.”