Strange video problem: Random standby mode switching

I have a brand new custom-built PC that I've assembled for the sole purpose
of playing games and absolutely nothing else (to the best of my budget, that
is). I'm having only one problem, unfortunately it is the most frustrating
one I've ever dealt with. Every once in a while, my monitor will completely
blank out and go into standby mode, seemingly randomly and completely
spontaneously (That's a lot of adverbs!). I've checked and rechecked all the
connections, and made sure that all of my video, sound, etc. drivers are up
to date. When I say randomly, I'm serious. Sometimes it will occur not once
during a computer session, and sometimes it will happen 16 times in an hour
(I've counted). That's the point where I give up and let it cool down for a
good while before trying again. From being in the middle of a game to
browsing the web, no time is definitely guaranteed safe. In fact, it's
happened to me three times (Make that 4--no, 5--no, 8 times now.) while I've
been trying to post this message, so I'm getting very frustrated (but I've
learned to use a text file to back up what I'm typing, so it's not as
frustrating as the first time it happened here). Also, the only way I've
found to recover from this problem is to press the power button on the case.
a short while after which I hear the Windows logoff sound and the system is
powered off shortly thereafter. Then I can press power again and it will
boot up all nice and shiny-like, as if nothing happened at all (But that's a
damned lie, and the computer knows it!!!). I'm tired of this, please help.

Stat-like thingamabobs:
AMD Athlon XP 2000+ (I'll be upgrading this and the RAM ASAP, seeing that I
underestimated)
512 MB PC2100 DDR RAM
Abit KG7 motherboard (not Raid or lite versions)
MSI GeForce FX 5600 (256 MB)
Sound Blaster Audigy Gamer
Windows XP Pro
Random old Dell 15" monitor (The only spare monitor that was lying around. I
suspect it to be the culprit, but have no means of testing another monitor)
blah blah NIC blah blah DVD-ROM blah blah hard drive
Black shiny case with window and blue neon light
(let me know if you require any more stats that I have not supplied)

Please do not critique my choice of parts based on your taste, unless it's
related to the topic of the problem. I'm new to the whole home-built PC
thing, and I'm very pleased I was able to get this far without much help;
but now I need more help, because what's the point of a gaming computer if I
can't hardly use it? Thanks. Sorry for being so wordy.