I've repaired more eMachines than I can count. All of the newer ones (black/silver, small 2 CD drive towers) have a bad motherboard when they don't post. I've diagnosed with new power supply, clear CMOS, working CPU, new memory, all drives disconnected, no cards in slots, video card in place of on-board VGA. Nothing will get this things to post. I replace the motherboard and every other part tests perfectly.
I've only repaired a couple that didn't need motherboards. Just something stupid. Hard drive, power supply, blown modem from lightning causing no post. Only one time, happened to be my sisters computer, the chipset heatsink hooks on the MB broke free from the solder. I just replaced the hooks and added extra solder support. Worked perfectly after.
Time for a new machine or motherboard. New motherboard will require rewiring for the front power switch, power LED, and hard drive LED.