I have had a Logitech wireless laser mouse for the last year and its great. The freedom from that cord is so great.
But I used to have the odd problem with it not working after I booted up. I spent ages playing with my batteries etc etc and going back to my old mouse. Then in a few days I plugged my Logitech cordless in and it worked !
I could not find any help on their web site.
Then one day I twigged it.
If ever your Logitech cordless fails to work, just unplug the wireless receiver from your PC and then plug it back in again !
You will find that Windows recognizes it again and you will be away ! (so simple and easy)