i can hear the fans and all but no screen and no sound

Hello
i 'm having a really odd problem with my imac and i haven't found the same problem in any forums etc...
anyways the imac is 20" 2.0ghz, 4gb ram, 2400xt and 250 hdd..
and the problem goes like this: when i leave it switched off for like 8 hours or something it doesn't open, i can hear the fans and all but no screen and no sound... i have tried what i read in the forums and mac's official troubleshoot site but nothing... what i have to do to get it started is switch it on with no screen and sound and leave it on for about 10 or 15 minutes, after that the boot sound plays and the mouse and keyboard turn on, then i unplug the power cord without even turning the mac off then i plug the cable back on turn it on and it works fine even if i restart it and even if i turn it off and on again... it just doesn't turn on if it stays for several hours off....
any help appreciated, thanks...