It may be the power supply, or simply the fuse in the power supply.
It could also be the motherboard itself since in the ATX specs the power button is wired through the motherboard.
Replacing a power supply isn’t hard as long as it’s a standard power supply and not a custom sized power supply.
I would say spend the few bucks and get a better power supply than the cheapest since you want to make sure your computer has adequate power, plus the cheap ones don’t supply constant power as they’re suppose to.
Worse case, if it isn’t the power supply you can always send it back, though if you have another power supply handy, I would swap them out first to make sure, just borrow it from your other computer.
Thanks. I was just curious if they are all pretty much a standard size and they generally all fit. NewEgg has this cheap one and it says “good for emachines” but it is too cheap.