Cully, and anyone else reading, power supply issues can be really really nefarious. While yes, power supplies can fail spectacularly with that textbook burnt tronics smell, they can also mostly work. They can even work but still send out occasional voltage spikes damaging other components.
Many moon ago a former incarnation of my computer started acting funny. I was slowly loosing components over a course of a few months. Hard drive, RAM, video. Eventually I figured something was up and busted out the mutlimeter. Things looked fine with it. SLIGHTLY high voltages, but all within 10% but I knew it was someting. So I retured the multimeter and busted out the scope. YIKES. Power spikes, dirtier than hell on the 12V rail. That POS was killing my computer slowly from the inside.
Had a friend once who had a computer acting nefarious as well. Occasionally restarting, bluescreening, crashing, just general ****ing him off. Multimeter said the PS lookd fine, same with the scope. But, throw a load on it, and the 5V rail just fell off the face of the planet. Looked good, but it couldn't support the hardware.
So Cully, I wouldn't write the PS off just yet. If you can, boot the computer with a multimeter attached to the 12, 5, and 3.3v rails. The voltages should remain pretty stable while it's running and actually thinking. If those look fine under load, then you can proceed to checking other components. In order of easiest to test, RAM, hdd, video, motherboard/pocessor