[i wrote the following while Thomas was posting his success above, but it is good diagnosis technique, nonetheless and may help someone else...]
If the standard things like resetting PRAM and the PMU don't help, buy a cheap hard drive and do a factory DVD install. If the crashing goes away, then it is software and you should reformat your drive and reinstall the software. Likely all that crashing has screwed up your system.
If the crashing does not go away, it could be anything: power supply, graphics card, hard drive, motherboard flaws.
Your factory DVD also has a hardware test. Follow the instructions printed on the DVD to access it. If it passes, you'll likely need to bring it to an Apple dealer to diagnose what hardware has failed.