I don't have the original install discs (must have lost them but they would have been 10.1 or 10.2 on Digital Audio, IIRC), but this is a full retail Tiger DVD (10.4.6), which I installed and then ran Software Update repeatedly until they told me there were no more updates.
I did a little more looking and I think I found the culprit (or at least part of it). There was a file missing from /usr/lib when I looked at the details about trying to launch Disk Utility. A little more research showed that this file is installed in the Security Update 2008-002, which I was pretty sure was installed (Software Update told me no updates were available). I do remember one botched update in the process of applying them. Perhaps that was it? Anyway, I downloaded that update (had to unpack the .pkg file on another Mac since this one couldn't), and ran the updater. It completed successfully, it rebooted, and now it works.
That said, if I find other problems I will probably just archive and install, but this is a hobby machine for me and there's no critical data on it. Thanks for the input!