I found out my problem. I didn't install GRUB via the Fedora install, which I found out how to do correctly now. I'm gonna have the bootloader put on sector 1 of the USB drive, then copy it out and put it as a file on the C: drive.
Yes, my BIOS does support booting from a USB device.
My only problem now is that whenever I go to re-install Fedora, the installation freezes while the files are being copied.
I'll get this thing working yet!
(I'm using steps similar to those in the first link above)