I restored the "links of interest" section by upgrading MT-Blogroll. I restored the OpenID sign-in by upgrading the OpenID plugin, though I'm not sure it works right. (Could someone use their LJ username to sign in and post a comment?) (I'm amused that I ran into the same problem installing it that I ran into last time. I went to post a comment on the OpenID Comments page to request that the documentation for installing be improved, only to find that I had already posted that exact request about 16 months ago. I now suspect that unzipping a zip archive distributes the contained files in the way that the author expected, while untarring a tar archive doesn't.)
Then I spent way too long trying to figure out why the blog about my father wasn't displaying properly. Finally fixed that.
I still need to go into the MT code and reinstate the changes that I had made to it before (especially the one that enables moderation for unauthenticated comments on old entries), and I still need to figure out why years before 2007 aren't showing up in the archive year-selector, but I'll do those things later in the week. For now, my blogs are back up and running. Whew.
Added later: Well, at least partly back up and running. It turns out that there's a bug in MTEntryNext in MT3.3, so navigation from each entry to the next is broken. The bug is fixed in MT4 (bug 46892 on that page), but that doesn't do me any good. I tried looking at the relevant code to see if they'd made an obvious change from 3.2 (where it worked) to 3.3, but the relevant code appears to be in the fetch_entries() function in php/lib/mtdb_base.php, which changed radically from one version to the next. So I gave up and filed a support ticket. I'm hoping they don't say the only way to fix this is to upgrade to MT4.