My New Build & Trouble

I am almost finished building my first computer and am still in the testing phase. It has a problem with rebooting itself during the strangest times. It seems to reboot at random times during internet browsing and during gameplay. I've only tryed a few demo games I've been able to download from the net and I've tryed playing Day of Defeat. It definaly ran longer playing the single player version of Castle Wolfenstien but It did eventually reboot. During online play of Day of Defeat it seem to run great for about a minute then It either freezes or reboots. But For running AutoCAD Version 2000 it runs fine. No problems for hours...but If I were to broswse the net or just search for files on my hard drive It will eventually reboot itself. I've downloaded all the newest windows drivers, my video card drivers, and I've flashed my bios. Anybody got any Ideas? Much thanks. Scott

Heres' what I'm running with.

GiGabyte P4 Titan 865PR MoBo 800 fsb
P4 2.8 800 fsb
512MB of Kingston Ram
Maxtor 40 gig hd
ATI 9700 ALl In One Wonder
HP CD Rom
NO FLOPPY YET

I've got an Antec Case that came with an Antec True Power 350 Watt supply. Is there any way to test the power supply? I'd hate to buy a new one just to see if the old one wasn't working properly.