cheap answer:
I tried all the above and more for my Logitech MX mouse including trying a 2nd Logitech mouse, different receivers, every USB port on my computer. One thing I did notice - the 2nd entry (created when the receiver is installed) under 'Mice and other pointing devices' had the same label as the first, 'HID-compliant mouse' and I understand it should have 'logitech' in its name.
Finally, I bought a (new) Microsoft mouse, installed the receiver, some software was downloaded automatically and my mouse now works. YES!! The device is labeled 'Microsoft USB Dual Receiver Wireless Mouse...'
All the many hours of research I did via google was via my XP with I/E 8 - very painful.
I would have really liked solving the problem myself instead of skirting it and I got fairly good at maneuvering around via the keyboard. But this is so much better and now I can badmouth Logitech at every opportunity.
BTW, it's incredibly annoying when someone poises an answer with a command that requires a mouse. While I finally uncovered the keyboard commands I needed it took time and there were still many times when I didn't know what to do and I just flailed about, sort of like the chickens one might see on the farm.