My iMac G5 Keeps Crashing

I have a first gen iMac G-5.
Over the last three months my hard drive kept corrupting.
1 HFS volume-unrepairable.
After going round and round with my local Apple Service Center (Apple dis-service Center) I finally got a new drive.
The computer has been going fine for about a week, then last night it crashed. While surfing on the web and watching Diggnation in a small window simultaneously it just crashed. Went to sleep, flicked the mouse and it woke up.
Now every time I "stress" the iMac it goes into sleep mode. By stress I mean, scroll through pictures in iphoto quickly, start imovie, surf and do anyting else at the same time, boom the computer crashes.
If I turn off the computer it will not restart.
I have to wait several minutes. Like it needs to cool down.
If this was a ATX case PC I would replace the power supply, it sounds like a bad power supply.
This was happening at the beginning of my hard drive problems, I think flaky power issues may have nuked the old drive.
Anyone have any ideas?

Have you tried to format & re-install? May be not the best solution but can be helpful.

Of course you can try things like formating and so on, but due to the nature of your problem....Or at least how you describe it, I'd take it back to Applecare and have it looked at. Sounds like hardware error to me.

You could try a re-install as suggested, although it definately sounds like a faulty power supply, or a heating issue (fans clogged/dying) or faulty memory. I would contact Apple if it is still under warranty.

I was thinking it could also be bad memory myself, as I had the local Approved Apple Service provider install 1 Gig of memory in January, all my problems started in February.
I have become an expert in mirroring my drive, I have done 6(?) complete OS re-installs in the last 2 months.

MY Imac G5 does the same exact thing, it crashes and lags regardless of what i have open. I see the "thinking" pinwheel thing more than my cursor. I dont understand this, I am going to replace the ram and if that doesn't fix it I will return the system.