Thanks everyone for your advice - I looked into it further.
When I don't have any other applications running besides xampp, there's no MySql or httpd processes, and web sharing isn't enabled. Restarting doesn't fix the problem, though it did at one point change the error message as described in a previous post.
I googled to find how to start and stop Mac OS X's MySQL installation from the command line, and tried the following:
sudo /usr/local/mysql/support-files/mysql.server stop
ERROR! MySQL manager or server PID file could not be found!
(no effect on trying to start MySQL from XAMPP)
sudo /Library/StartupItems/MySQLCOM/MySQLCOM stop
Stopping MySQL database server
Which still had no effect on my XAMPP problem, but I was surprised to see that MySQLCOM was in my startup items folder at all - it doesn't show up in my login items control panel. I tried to drag it out of that folder, but it's apparently read-only; I can delete it, but I'm afraid it might be read-only for a reason and doing so would break something. And if there are no mysql or httpd processes running, it's possible it's not affecting things anyway.
My friend had tinkered unsuccessfully with trying to get MySQL started months ago before I found XAMPP, so while I thought all the changes had been backed out, it's possible there are one or two vestiges of that process around.
Any thoughts? Thanks again.