The failure to power up may be caused by corrupt NVRAM brought on by a flat battery, as the earlier posters suggest. However, the crashing you experienced is probably a heat sink issue as John suggested.
The heat sink grease Apple used on PPC601 chips dries out and stops working after a time, usually much shorter than now. Carefully, did I mention carefully, carefully, unclip the heat sink from teh CPU card. Examine the heat sink grease. It is probably white and powdering at this point. Clean it off with swabs and alcohol and replace with a small (small) dab of new grease. Do not overapply, as the stuff is only filling the tiny imperfections between the heat sink and CPU die caused by the two surfaces not being perfectly flat. If the stuff runs out onto the PPC601 pins it can cause shorts. I killed a PCC Power 120 motherboard this way many years ago.
Be careful when replacing the heat sink. Excess pressure can crack the CPU package. A common failure mode for PPC601s is for them to crack. Oh, while you're replacing the heat sink grease, you might look carefully for cracks in the CPU package. Your problem could be cracking rather than overheating, but I would bet on overheating.
The heat sink grease problem seems to show up most frequently on 7100s for some reason.
I had one back around '99 or 2000 that drove me crazy. It would run great for a little while and then crash or lock up. I replaced the system, etc. I don't know how many times. Then, once, it showed video artifacts which I recognized from an overheating system I had worked on and after that I found the worn out heat sink grease.