I figured out what the problem was, and it had nothing to do with the mouse being made by Dell (besides, Logitech was the company that manufactured it, though it was a Dell product). The problem was in relation to drivers installed by software to make a PS3 controller work on my PC. When the DualShock 3/Sixaxis drivers got installed, it messed with the integrated Bluetooth and caused it to not recognize any Bluetooth devices at all.
If anyone else has the problem and has installed MotionInJoy and the drivers with it, you will have to try to remove both and restart your computer. If restarting doesn't work, restore your computer (if possible) to a time prior to installing MotionInJoy & its drivers or (if necessary) back up all of your files and restore it to factory defaults. That will fix the problems.