Well, I did some reading online, and with other people who had the same problem as you (lights blink, but that's it, nothing else works), they had to replace the mobo in their emachine.
I wouldn't run out and buy one just yet though. I'd strip the tower down to bare bones, leaving just the hdd, fans, 1 stick of ram, mobo and cpu (with fans of course) and try to power it up. If it fails to start, then swap out the stick of ram with another stick that you know will work (one that is compatible with your mobo). If that fails, then I'd stick everything back in it (rather, just reconnect the optical drives, floppy etc.) and pull the cmos battery for at least 10 minutes, then reinstall the battery and try to reboot.
If you do have to replace parts, ensure that they will fit in your case, as I believe that emachines are propietary when it comes to some of their hardware components.
Hope this helps, let us know how you make out with this!
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