I have a logitech mouse and the exact same thing happened. What hangs it up is when it's trying to reconfigure while windows is loading. I think if you'll open it in safe mode (maybe more than once to get it completed) you'll get it straightened out.
It's still got a bug or two...and I think it's from the logitech auto update feature. I purposely told it NOT to install that, and I noticed it did so anyway.
But try opening windows in safe mode, and if it finally does load, then run a scan-disk just to be sure.

Good luck.