Comp shuts down when starting game. Issue with PS/GPU/Other?

So yea, got this little crap comp set up for my parents. But the other day I tried to load this crappy little 2d/3d top down game that my gf and I play so we could play together.

The game installs, starts up, you can log in through a launchpad program, accept terms and conditions but when its about the load the zonelist/serverlist, a little dos command black window pops up and the computer crashes and reboots.

This happens EVERY time I try to load the game.

The game is Cosmic Rift. The computer is an old Compaq Presario 5004ca. It's a P3 950mhz Duron CPU with 8mb Vid and 256mb Ram. I know its crappy but my parents only use it for BASIC net browsing and email... thats it... And the game in question requires much lower spec's to run. (I had the game running on a 120mhz with 32mb ram with ease...)

Related Info: The computer routinely freezes for like 5-10 seconds then the monitor blacks out and comes back on and the computer regains useability.

Is this an issue with the Power Supply, or the video card? I can't think of any other reason for it to shut down like this, and hang with the monitor flicking on/off.

Thanks in advance for any and all help.