I have 'exactly' the same problem and have searched high and low on the net for some explanation.....no joy...
I have a 3GB P4 with 512MB RAM and had no issue with GTA III. I am also running it with a ATI Mobility Radeon 9700 graphics card and I know there are registered issues with this card and this game, but I tried all of the 'fixes' suggested and the Patch to no avail, still a few minutes of play followed by 'bluescreen'.....
I anyone 'out there' has a cure, let me know and I will 'spread the word'....