Okay everyone, I got together with another tech who had replacement processors, but it turned out to NOT be the processor. We tried replacing the memory, the power, everything but the mainboard (because he didn't have any of those). We concluded that the mainboard was the issue.
Now, seeing that I put this system together over four years ago, I didn't think I'd find the same board again. I verified that the board has been discontinued (an ASUS P5KPL-AM). However, having looked up the specs, I've found a comparable board available on ebay.
For those who'd like to donate toward this, I have paypal. You can send money to me that way using my email address (firstname.lastname@example.org).
Thank you everyone for your support and emails.