From what you have written above there has been a wide variety of matters for the PMU to think about. The constant litany in Apple's literature for techs and wannabes is, if a New World Mac declines to start up, let the smoke clear and then reset the PMU. That's only slightly more painful an exercise for a slot-loading iMac than it is for a G4 tower, but it is also most often effective. The secret is, having deprived the Mac of both mains and battery power for at least 10min, that you press the PMU switch once only, without bouncing it by being tentative, for a second. None of my chilluns mentioned above, nor a 400MHz Graphite, ever failed to respond to such housekeeping. You have already been canny enough to allow the iMac breathing (or convecting) room, so if it will not respond to resetting the PMU you are obliged to conclude that there is indeed a debilitating hardware fault. Given that you probably know little of the Mac's provenance, that is entirely possible given that the FBT and PAV board are its statistically prominent failure-points as a result of overheated lives.
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