Emachines has well publicized problems with some of their motherboards. These boards are made by Tri Gem, and usually are also installed with a Bestec 250 Watt PSU.
Many later Emachines have a Bestec 300 Watt PSU which doesn't seem to be lethal to the board when it fails, but make no mistake, fail they do!
Part of the question is actually which Emachine boards fail and take out the PSU, not the other way around. The Emachine number you give seems like a later model, and you might luck out with just a bad PSU.
I had a Bestec 300 fail on me and the Emachine is still running fine. But, it's a T-5026 with an Intel board.
An Antec "Earthwatts" EA-380 (Watts) might be a nice choice. Unfortunately,you just missed a great sale, . As long as you're not going to try and stuff in a high end video card, any decent quality 350 watt PSU is plenty for your rig.
Since Intel's 845 chipsets/boards only offer an AGP port for graphics anyway, it probably wouldn't make sense to consider an upgrade, since not much is available in the way of AGP cards anymore
Here's an Antec "Earthwatts" EA-430 (Watts), $35.00 if you don't mind waiting for a rebate. That's actually $25.00 less than the EA-380 at the moment.
http://www.newegg.com/Product/Produc...82E16817371006