To merlin_2:
The operating system is Windows 98.
What happens is this: When I power up, I can hear the computer start to come to life. After 5 or 10 seconds, it completely, totally stops. The screen is blank. The fan stops running. The hard drive doesn't move. Everything comes to an absolutely halt.
I then clear the BIOS, by moving a jumper. I power back on, and the system starts. All the BIOS settings are OK, and nothing has changed in the system since last time. However, the BIOS setup screen prompts me for memory type, and time/date. I simply re-save the settings, power down, put the jumper back in the right position, and power up. I get past the post screen, Windows starts and everything runs fine.
But the next time I power up, I have to go through the same procedure again.
I had hoped that replacing the battery would take care of this, but it made no difference. And again, when I'm prompted to go into the BIOS setup screen, all settings are fine. The time/date is correct, even though I'm prompted to re-save it. The hard drive settings, video settings, etc., are all OK.
I'm pursuing the tips on the help screens that Computer Commando provided, in hopes that will lead to something. So far, nothing seems promising, but I'm still working at it.