When we don't have any such desires that don't have an answer (e.g. hunger) then I think it does indicate that such an answer exists. I don't think it makes much sense otherwise. [...] Well I think it's probably very debatable whether naturalism best accounts for art / beauty and particularly, morality [...]
Human beings like finding interesting and appealing ideas because we're naturally curious. Culture is a mechanism which propogates interesting ideas around. Why does art and philosophy need anything besides this as an explanation of origins?
Morality has obvious benefits: if you can assume your neighbour will be nice and that you should be nice to him, you both benefit. More wide-ranging kinds of altruism are explainable as cultural adaptations of this drive. It's not as though every single thing we do needs to be directly traceable back to a biological origin; culture is more complicated than that, and has adapted many previously survival-oriented drives (i.e. the sex drive, protection of your offspring) to new ends (sex with contraception, adoption).
We know that culture exists, and a fair amount about how it operates (though there is much more to be discovered). The same can be said about the human mind. However, this definitely cannot be said about a creator God; to my understanding there no facts which necessitate the existence of a deity to explain, or which are best explained by a deity.
It's certainly true that you can introduce a vague, distant, or non-interventionist God without contradicting evidence, but doing so is just as arbitrary as introducing Last Thursdayism.
As I said, the poker scenario presupposes chance, which is begging the question somewhat. If I found $50 in my letter box instead of the usual junk-mail, would I suppose chance or intention?
The existence of life on Earth is only remarkable to us because it's our existence we're talking about; if we lived anywhere else, our existence there would be just as remarkable to us. To make the appearance of $50 in your mailbox a comparable situation, you'd have to first go from house to house looking for one with $50 in its mailbox, move in there, and then exclaim about the improbability of finding $50 in your mailbox.
#1 - there is a difference between believing something will happen, and believing something has happened. And indeed, believing you've experienced something. The disciples didn't die for a belief they 'hoped' was true, they died for a claim that they experienced something.
So does this make the beliefs of the Jonestown residents true as well? That situation also met all your qualifiers: people had a religious experience (faith-healings and similar activies performed by Jim Jones) which they believed in so strongly that they died and murdered for it. There have been numerous other such situations in history; are their beliefs also all true? Here is a good blog post discussing this in more detail.
And of course, if someone was reporting that the resurrection happened, then they would simply be written of as a believer too, wouldn't they? Asking for confirmation by someone who didn't believe it happened is a little absurd to my mind.
Even a disbeliever would've noticed the existence of the guy and his quickly growing following. At a minimum, I'd expect there to at least be some historical note somewhere along the lines of "This guy who claims to have been resurrected according to some Jewish prophecy is wandering around the city with a bunch of his followers", since there was documentation of a similar nature for other religious figures of the time in that area of the world. See here for more on this.
Also, sorry Andrew, the link you gave to another blog post appears to be broken.