I guess my Firefox 2.0 profile was a bit corrupted.
I had noticed that the "Search This Blog" API on my sidebar had not been loading for about a week.
It would just bring up a little "...Loading" dialog but never resolve.
Today I tested it in Internet Explorer, Opera, and Minefield, and it worked fine.
So I launched up some various Firefox 2.0 "portable" builds and it worked fine in them as well.
So I started troubleshooting by disabling the likely offending parties, NoScript, FireBug, AdBlock, etc. and restarting. None of that made any difference.
So then I disabled ALL my extensions and restarted.
The Google "Search This Blog" function still wasn't working.
I restarted a few more times and it popped to life! Temporarily. Then it stopped working again.
So I backed up my profile, uninstalled Firefox and installed it fresh.
Still not working.
So at this point only thing I could consider was that something was definitely scrambled in my profile.
So I deleted my profile folder's contents and copied into it an almost exact duplicate I had built from another "portable" 2.0 build.
Launched Firefox 2.0 again and now it is working again.
I did have to go back and do a few manual reinstallations for some extensions that didn't quite survive (functionally) the brute-force copy of one profile folder into another, but overall it did work and most all of my settings and preferences were preserved.