Sorry for a confusion, it can be a logitech problem - both keyboard and mouse are logitech and I had an option to check different manufacturer and it worked at the windows login page.
I have a similar, maybe even the same issue with Bluetooth. The Bluetooth doesn't work at Windows start. My Bluetooth mouse doesn't work when I log into the windows. To make it work I need to use a keyboard, go to Bloototh settings, and try to add a ...
