It probably belonged in the Mac OS forum, assuming it is a software problem. However, if it traces to a hardware problem, then it belongs right here. After we finish figuring it out, we'll be sure to make a final decision.
I'm thinking that it was either disk damage or a permissions problem. Since you aren't having luck from the Tiger DVD, try booting from the Panther CD and use Disk Utility from there to repair. The best answer would be to repair with Disk Warrior or TechTool Pro, if you have either.
If it passes a repair, then you should also repair permissions before attempting an update install. If you elect to erase or to archive the install, I don't think funky permissions would matter. Doing the lobotomy wasn't the best solution here - I assume you deleted the /Library and /System folders.
However, it could be the hard drive giving trouble. In Disk Utility, select the drive in question and look at the SMART status for that drive.
A status of "confirmed" or "drive is working normally" is good, nothing to worry about there. Messages such as "SMART: failure imminent" or "this hard drive is about to die" or "sell the house and buy life insurance RIGHT NOW" means the drive is going to die really soon.