It's hard to tell without seeing it. No form factor for the existing psu on the manufacturer's website:
http://support.gateway.com/emachines/desktop/2009/emachines/ et/ET1331/ET...

I recommend contacting support directly and ask them if an ATX standard power supply will be compatible with the case of your system.

Actually, a real easy way to confirm it would work is if you measure your existing power supply against these measurements:

http://www.evercase.co.uk/PowerSupplyMeasurement.htm