|It's likely the power supply. Many of those emachines came with crap power supplies. If you have a working compatible power supply you can swap in, that would be the best way to test it.|
Unfortunately, sometimes when a power supply goes it ruins the motherboard as well but you won't know that until you try another power supply.
Another thing to look at is the motherboard capacitors, especially the ones surrounding the cpu. If they look kind of 'puffy' like a soda can that's been in the freezer then they are bad or going bad and might be the cause.