iMac shuts down during startup, but consecutive startups do work(+vid)

Here's a Youtube video showing the problem (problem at 0:42): http://www.youtube.com/watch?v=dvZ57VSR1...

So basically what happens is when I turn on the iMac, as soon as it starts loading the system it will turn itself off after a flurry of white noise on the screen.

Subsequent boot attempts bring it gradually closer to a full boot, until it completes after about the 5th attempt.

This seems to be video card related. When it's booted up, there are graphics glitches on the screen; doing something video card intensive causes more glitches, and starting the screen saver causes it to shut itself off.

However, after about 15 minutes of being turned on... everything gradually turns to normal. The machine itself works perfectly after that! I don't see glitches anymore, I can use graphically intensive apps.

So this is an extremely weird problem. It's almost like it needs to warm up for a while first. Of course, that can't be it.

It must somehow be tied to the video card. Also, when I hold down the option key during startup (this brings up the "choose startup disk" screen), I can keep the machine turned on for as long as necessary without it crashing (presumably it doesn't yet use the video card at that point). So if I hold down the option key and keep it on that screen for a while, and then boot, it completes the boot in one cycle.

It would be great if someone could shed some light on this!