Ed,
I admit to being somewhat perplexed by your experience. But let me ramble a bit here anyway.
My opinion is that problems of the sort that you are experiencing (freeze after a software update) are almost always due to some software problem. (I base this opinion to a large extent on the experiences of other people in these forums.) The fact that your system works okay with Tiger is consistent with this idea.
But, if it is a software problem, why did it not go way when you re-installed Panther? I am wondering how you did the re-install. Was it an Archive and Install? That is the easiest approach and the first one to try, but there are some things it cannot fix. For one, if user settings and preferences are maintained during the A&I and the problem is related to these settings or preferences, then the problem will remain. In that case, an Erase and Install would be needed to clear out everything. Of course, this also deletes all of your data, so it is something you do not want to do unless you have a backup (which you said that you have).
Another thing that an A&I cannot solve is corruption of the filesystem (computer loses track of where some files start and stop on the hard drive). This problem can usually be detected and often repaired by booting off your install CD and using Disk Utility to repair the disk. You said that you used Disk Utility but gave no other details. I take that to imply that you detected no problems. If there are problems and Disk Utility is unable to fix them, a more powerful utility can sometimes do the job, and sometimes there is no solution except to reformat the hard drive and re-install the operating system. This of course destroys all data on the drive.
If there were a hardware problem behind this, the most likely thing in my view would be some bad blocks on the hard drive. I am pretty sure that Disk Utility, as used above, will look for bad blocks and mask them out if any are found. You mentioned something about 1 Gig of RAM. I think that RAM is unlikely to be the culprit. Problems with RAM usually are manifested as more erratic behavior that what you are experiencing.
You have already exhausted many of usual tricks, so what are your options? It sounds like you do not want to buy a copy of Tiger just to fix this and I can understand that. So, you could go to more and more extreme versions of re-installing your software. By this I mean using your Panther install disks to do an Archive and Install, then to do an Erase and Install if the first did not work, then to reformat and do an install if the Erase and Install did not work. Before doing either of these last two step,s you want to be sure that you have backup that you know works. You have said that "re-installing Panther does not fix the problem" and also that you "haven't done a system restore". It is not really clear to me what you mean by re-installing Panther. Was this from a backup or from your install CD?
If you want to avoid a re-install from your install CD as long as possible, then my suggestion is to attempt to troubleshoot the problem further by booting into Single User mode (which I think you have done). Once you get the disk mounted, I would suggest looking in the system.log file for an error message. Once you have mounted the disk, you can look at the end of the system.log file with the command
tail /var/log/system.log
Look to see if any of the messages look like they might be indicative of a problem. If you see nothing, you can print out more lines by doing this:
tail -40 /var/log/system.log
which will cause the last 40 lines to be printed. If you see any message that might be hinting at a problem, post it back here and perhaps someone will get a clue. I should say at the outset that this way of doing things takes a lot of patience and is not guaranteed to provide a solution.
I hope this ramble helps a bit. I know your are frustrated and I hope you get a solution soon.
Rich