Strange power on problem

My Imac Core2duo a1224 has a big problem .

When I press the power button, a cd rom check is heard, and then nothing ... completly dead, nothing on screen, and no fan spinin…

If I leave it for a few hours, some time the system boots normally, but the fan spins at the highest speed….

So I can use it "normally" after that (except for the annoying fan noise). But, If I turn it off, I can power on right away, but if it stays off for a few minutes the same thing happens again.

Sorry for my bad english :)…