I have a special tool for fixing such a computer. I call it the Justice Machine. 1 potato stuffed into a 2"x4' barrel accelerated by 100+ psi of compressed air will take care of your problems right quick.
Really though, I had a similar problem with an E-Machine when I worked for Circuit City Firedog. They hardly provided the techs with any extra hardware to test with there, and after ordering in a replacement MB, then later replacement RAM (both with no success), I asked that the parts provider send a new CPU, PS, and HDD, because the customer was not happy waiting (which I understand, even though the policy clearly said it could take up to a month). Replacing everything with the new parts fixed it, then I tested with the old HDD which was fine. I would have liked to have troubleshooted more to find out what exactly was wrong, but the techs were very understaffed there, so that wasn't reasonable.
I believe it is possible for a bad CPU to prevent power on. You can't trust the boards and builds some of the OEMs sell to provide normal diagnostic features like beep codes either unfortunately. Considering the specs on that beast, it probably isn't even worth your time to continue pursuing it. There's used PC places that sell better systems for so cheap in most big cities.
... I was just thinking back on that one I repaired at CCity again, and now I'm sure it was more complicated and I believe that it involved grounding problems which permanently damaged the first replacement MB. It was one of the more difficult repairs I have worked on, which makes the case for complete replacement even stronger. Good luck if you decide to continue working on it!
