Well....I think I found the culprit. I yanked out the video card, and the unit booted up flawlessly several times in a row. I ran it from another mac, using "screen sharing". Played iTunes, and accessed some various files with no problem. Stuck the video card back in, and it booted up rotten again. So it's either the card or the PCIe 16x slot. Not good if it's the slot.
Early 2008 Mac Pro Processor: 2x2,8 Ghz Quad-Core Intel Xeon Memory: 8GB 800 MHz DDR2 FB-DIMM Graphics: ATI Radeon HD 2600 XT 256 MB Software: OS X 10.9.5 (13F1077)