Could my iMac possibly just have a temporary case of heat stroke?

Question

After working on my iMac off and on all day, I left it up and running when I stepped out of the room briefly and returned to find it had shut down. This particular Mac is networked to a PowerMac G4 and dual core iMac, both of which seem to be working fine .. . (as was this one, until this problem started).
Hitting the power button did not get it up and running, although the chime seemed to work; however the screen remained black. It was hard to tell, but I also think the power switch was working a little erratically, because at various times it seemed like it required eiher a "forced quit" and restart, restart with the shift key on — or sometimes just a restart alone to ring the chimes. Bottom line though, was that while the on button sometimes lights up, the screen remains black.
Unfortunately, my optical slot drive died about six months ago which is how I ended up with the dual core iMac — but so far have not used it much, since most of the software I normally rely on is not yet available for the new model. So instead, I have been switching back and forth from one computer to the next, as needed. However, because of the drive problem, I have been unable to boot from either the hardware diagnostic or system CDs to look for or repair possible errors.
Although the two iMacs currently are connected via Firewire, I have not yet taken time to see if I can transfer and save the most important data — hoping to get all systems up and working properly first.
More importantly, I'm also hoping one of you Mac wizards will tell me the problem is just weather-related, since the temp outdoor has been in the low to mid-90s all week and probably even hotter indoors. Is there any point in just letting things cool down overnight instead of repeatedly hitting the "on button" . . . or does it sound like my goose is really cooked?
Anyone have another idea of how I can rescusitate this machine?

Answer 1

Update:
Sorry to report that while I waited in frustration for some sort of response, my iMac gave up and died.
Since initially it looked like it might "only" be a power problem (not worth repairing, as the CD drive also pooped out about 6 months ago), I was arranging to have the drive reincarnated as an external drive, only to learn that the drive, too, was on its last legs. I have no way of knowing what's on the drive, so am still trying to decide if it's worth paying for data recovery. Luckily I think have backups of the most important doocs.