System halts after shutdown, need to restart in Safe Mode and clean Files00*

Sorry, I don't know if this is a s/w or a h/w question:

It seems every time my wife's pc is shutdown (certainly every bad shutdown -power outage, etc.), it will not boot back up; it either goes into a cycle of constant restarts or halts at a blue screen. I then need to boot in Safe Mode, delete all the bad files (File001, 002...) and restart. Then it boots up fine till the next shutdown.

I have never had problems like this on my other pcs even when they have had bad shutdowns.

Could bad/damaged memory be causing this?

What would?

Thanks,
Scott

 

What OS? Plus any other hardware stats you may have.

 

Sorry I forgot these details:

Win2K, very clean pc (no adware, spyware, malware, viruses, trojans, etc.)

It's just for her e-mail and web research. We run Avast AV and Sygate FW.

Thanks for any help. I don't know why this one pc is so flaky, and all my others are just fine. That's why I thought it might be something like RAM, except that the pc runs fine once it's booted up.

I'm clutching at straws here.

Scott