Problems with power button and sleep

The other day, my Imac G5 would not power up. I unplugged it, tried a different outlet; all the obvious stuff. I have it set up to start up at 10am and shut down at 3am because I've had problems in the past waking it from sleep mode. At 10am, the Imac started up as normal.

Today- I was able to turn it on using the power button. I know there is something wrong with my Imac, and sooner or later I will have to fix it. Based on these symptoms, what could be going on here?

Check out the thread right below yours "random shut downs"
My guess is y ou're having the same power supply problems most early generation iMacs had. go to the link in one of the replies to see if your maching qualifies for a recall