Well, in case anyone is reading this later, I fixed it myself. I read some answers to other posts and did what I obviously should have done all along.
I overwrote all the files in the directory with the new 2.7.1 ones; moved in my theme and plugins, replaced the wp-config file with the one from the backup that did actually get backed up, and it worked. When I activated the plugins they worked as well (although e-commerce took a bit of mucking around.
