That unit takes a proprietary power supply which is very difficult to find, is not of a standard size or dimension and cannot be exchanged for a standard ATX power supply. You best bet is to contact emachines for a replacement or start over with an entirely new machine or at least a different case and power supply.
You can probably find replacement units on ebay, but they're likely to be used, even if they say they're new, and you have no real guarantee of fitness of the unit if it dies in two days or two weeks.