Resolution problem solved
Although I would be happy to have any light shed on this situation, my purpose in posting is just to get this rather odd problem and my "solution" on the web so that if someone else has the same problem, they might find this posting and it might be of some use.
I have an old Thinkpad A30, running Fedora 7. It was working fine and then suddenly was coming up in the wrong resolution, and it was quite low - like 800x600, and the standard tool didn't list any higher resolutions. I fiddled with xorg.conf, but that didn't help. Then suddenly, it started working. The problem didn't go away, but it was sporadic.
After seeing it come and go for several weeks, I finally figured out what was affecting it: If I turned the computer on while the power cable was plugged in, I had the problem. If I turned it on so it started the boot running off the battery, then it would not have the problem. It appeared to be OK as long as it wasn't plugged in at the very beginning, although I didn't try doing it immediately after hitting the switch.
Anyway, the fix (kludge) is pretty clear - just unplug the thing before you turn it on (or reboot). As I said, if anyone has more insight into this, great, but in any case, I hope this posting is useful to someone out there, someday. Meanwhile, I'll write it off to a hardware problem.