imac shutting down

I have a 2001 imac that has been shutting down on its own a lot.Had it sent back to apple came back and now its doing it again but this time it will not boot up passed the gray screen. it will come on make the start up sound turn to the white screen and i will see the apple icon the it will shut back off and will not reset till i unplug the power for 10 mins. Is therea way to hard reset it will it is doing this or will i have to reset to factory and if so how.

Thanks