It sounds like it could be a bad power supply. The problem is, the power supplies on those emachines are most likely a Micro Atx which isnt something you can get somewhere like bestbuy. They are pretty cheap though, new egg has a bunch for a little more that $20.
http://www.newegg.com/Product/Produc..._-NA-_-NA-_-NA
With that said, it could also be a bad motherboard. I just finished working on a similar situation. I bought the new power supply, and it didnt work, I ended up having to swap the mother board.