I have 2 eMachines (desktops) that I am currently trouble shooting. I suspect that in both cases the start microswitchs behind the front panels are the culprits. The final symptoms are neither computer will respond to the start button. Later I will report the results of further tests once I get access to the microswitches.

Have you confirmed the power supplies and motherboards are good? The most common problem I find with the eMachines that end up on my bench are low quality power supplies that last just past the one year warranty. In twenty plus years, I've only replaced two or three switches. If the switches are actually bad, that's a new low even for eMachines.