I have an eMachine W2228. The power supply starting making strange noises one day and the next day the PC was dead. I swapped the power supply and as soon as I plug the power cord into the back of the PC, it powers on, the CPU fan spins but I see nothing on the monitor (and the monitor is good). It doesn't want to perfrom the POST. I swapped the RAM with known good RAM and no help. I double checked both power connections to the mainboard to make sure they were properly seated, no help. There were no hardware or software changes done before the power supply died. I'm thinking that when the power supply died, it surged the mainboard and did some damage...Any suggestions? Thanks!
One more thing to add, before the power supply died, the PC would turn off and on by itself!

The noises was probably the PSU as you noted. The on and off again is probably the result of a bad or (by now) a burned out solder joint, which means from your pov it's a new system board.
The BIOS chip is probably toast by now also, to test for any kind of post, you'll have to get an exact duplicate. May or may not help, considering the aggravation I wouldn't bother.
While it's a bit late in the day for that mobo but you might check for dust/lint contamination on the CPUs cooler fins.