I've been through some tricky experiences with Logitech!
My suggestion would be to first cleanly uninstall the drivers and any other Logitech supplied software, then shutdown. Remove the Unifying Receiver for use later on.
Plug in a standard, wired, USB Keyboard and Mouse to the rear USB 2.0 or 3.0 ports and reboot.
Go into Device Manager...
Delete all the USB devices that are mouse related (Mice and other pointing devices,) using the keyboard to toggle between selections. Finally delete all the USB controllers (the keyboard will lock up, no worries.) then power off for 15 seconds and restart the machine with just the wired Keyboard and Mouse attached. The USB and related ports will Plug and Play, so be a bit patient.
Now, turn off the Mouse and Keyboard (if wireless) and switch back on.
Plug in the Unifying Receiver to any back port - USB 2.0 is best, so you can use the 3.0 for other faster items.
There is a software to download from Logitech that lets you manage "Unified" devices if the wireless mouse and/or keyboard work. I suggest downloading and installing it, if you can. There you can adjust a few Logitech specific things if so desired.
Let us know how you do.
Thanks!
