I realise I'm coming late here to a discussion that has veered wildly off-topic into lord knows what.....
But to the original question, I would say September 1, 1939. Hitler himself and the Nazi party may have been doomed with or without war, I can't speak to that. But once war was joined in earnest, I don't see any way they could have won.
They were never going to have done anything significant to Britain (Sealion was of course completely unrealistic, and the inability of German planes to reach Northern England and Scotland meant that a German victory in the Battle of Britain would have been fairly meaningless).
North Africa was always going to be a dead loss because of the lack of logistical capacity.
And once he shared a border with Stalin, I don't see any way that war between Germany and the Soviets could have been avoided, even if Hitler was assassinated and replaced by someone eminently more sane. The more I've read about it, the more I think that Barbarossa was actually pretty much as successful as as an invasion of the USSR could possibly have been (at least the 1941 part anyway). I don't think the original plan based on a thrust straight to Moscow would have been successful - they didn't have the logistical ability for a significantly faster push to Moscow, and if the Soviets defended it then it likely would have turned into another Stalingrad (in any case, I don't think they could have taken it before winter 1941 - reaching Moscow and taking it are two very different things). And even if they did somehow take it, I don't think it would have been such a knockout blow as they intended (it was pretty much evacuated by the time the Germans got near anyway). I think they went with the right plan by going for the destruction of the Red Army as the first priority in preference to spearthrusts straight at e.g. Moscow (a plan even more predicated on the idea of the Soviets just throwing their arms up in despair and defeat), which just would have left them with a whole bunch more Russian troops left to fight along ridiculously long and exposed flanks. But really, I think they had no chance no matter what the plan.
As a backup date, I'd say December 7, 1941 - since if Hitler didn't defeat the Soviets in his initial push before the first winter (by whatever means that might have happened), he was never going to; and getting the Americans involved just massively sealed what was already a fait accompli.
Hitler was never going to have a better chance than 1941, since any further delay would only have increased Soviet readiness. And I can't imagine Stalin not attacking Germany as soon as he felt he possessed the advantage (though I'm not convinced he was planning an attack in 1941) - here's his chance to be an aggressive warmonger and take massive amounts of territory, while getting to play the white knight card at the same time. He was not the sort of guy to turn that sort of opportunity down.