The understanding (Jeff Levi radio talk show on computers) was that e Machines use proprietary hardware. Cases and power supplies are among them. Im surprised that you were even able to mount the PS in the e Machine's case. You probably are better off finding an eMachine authorized service center and having it repaired there.
He, Levi, wasn't quite correct on the whole. The emachine power supplies aren't really proprietary. I've replaced numerous ps's in old and newer emachines with stock ATX power supplies and have never had a problem. What is proprietary is the front panel connector---the pin out on the mb and the connector from the case are completely different that what is found on "standard" motherboards.
All you need to do is pull the power supply out and test it by shorting the green wire to ground its possible its not the power supply, also if it is true that it takes a proprietary emachines power supply you can get them on ebay for cheap.
One point....look at the power supply's label and ensure that the ps doesn't need to have a small load placed on it. You can figure this out if the ps's label, where it lists the voltages and load ratings for the ps, has listed a minimum amperage for the ps. Not uncommon for older style ps's to have that requirement, so if you try the jumper trick on one of them, it won't turn on even if it's perfectly fine.
If it does list a minimum load, plug in a fan or two before trying to turn the ps on. It's also an easy, quick way to see if the ps is turning on...