I figured out a way to get around this problem.
Uninstall XAMPP, (it's not working anyway, right?), then reinstall using the Windows Installer version download. This one:
http://www.apachefriends.org/download.p ... taller.exe
During the install, at the "Choose Install Location" screen, change the destination folder from "C:\Program Files" to "C:\.", (NOTE: there's a DOT).
The installer will see this as a valid directory, and will enable the "Install" button so you can continue on. It will actually install everything into "C:\xampp", and works because the dot stands for the current directory, (in this case the root). You COULD enter an unbroken directory name like "C:\xampp", but then you'd end up installing under two directories like "C:\xampp\xampp".
Afterwards, I didn't have to run the setup_xampp.bat file. I just started it up with xampp_start.exe immediately after the installer finished. Worked the first time, no problems. All default servers were running, and all the demo apps worked...