I have similar. 'fatal' game-starting crashes (even though under error-report, I unchecked 'automatically restart). I also have somewhat similar specs as the OP. I can play Demigod for up to about 45 minutes, but it will crash anywhere from 5 seconds to 45 mintues into the game, resulting in a restart of my computer. Here's my specs
Win XP
AMD Athlong 64 X2 Dual
4 gig ram
Sapphire ATI Radeon 3850, 512 mb, agp slot
All my processor drivers (including AMD dual-core game optimizer), chipset, video drivers, sounds drivers, everything I can think of is up to date. I try playing with my security software (Bitdefnder) off and on to no avail. I have a brand new PSU (pC Power and cooling) that far exceeds the power limits. I have more than enough cooling, with extra fans optimized to work together to carry the hot air 'up and out'. Like someone else mentioned above, most other games work fine, such as Left for Dead, Dawn of War 2, and Lord of the Rings Online. All three of those games I've had marathon 12+ hour in a row play sessions with no problems whatsoever, and the graphics settings turned up fairly high. The only game that had anything remotely like this was Sins of a Solar Empire (which I understand are made by two different devs, just a common publisher in Stardock)... Sins I just gave up playing, I couldn't play for anymore than 5-10 minutes before the fatal crash/re-start bug.
I've gotten in touch with Stardock support and just sent them some DirectX Diag and startup files they requested. Also, once, my pc didn't restart after the crash, and I was able to salvage a Microsoft error report, which I also forwarded to Stardock support.
My heart really goes out to those who aren't able to play this otherwise very cool game. I'm starting up work and school soon, so I won't have much time to play. However, I *would* like to figure out what's causing this, if possible, if for no other reason than I love building/fixing/troubleshooting pc's. THe OP gave me a glimmer of hope, in a way, in that it may possibly be a similar bug in each of our machines, and hopefully in that commonality, a solution might emerge down the line. And not at all blaming the devs or Stardock here -- would just like to get to the bottom of things so I can play Demigod for more than 45 minutes 