I use Knoppix 3.6 (it worked with 3.4 too), I would assume there shouldn't be any major differences between them.

Assuming the following:
1. You had a working installation either to HD or with persistent configuration
2. You changed your mouse after this installation

I would do:
1. Boot from CD and see if the new mouse is properly detected and configured
2.1. If the new mouse works booting from CD, then you need to check the resulting configuration files vs the persistent ones to see what needs to be adjusted.
2.2. If it doesn't work there are 2 options:
2.2.1 You have a hardware problem (try the new mouse under Windows to see if it works)
2.2.2. There may be a driver problem. In this case you'll have to Google or check in the Debian site for additional information on your particular mouse model.

Wireless mice are tricky and susceptible to intereference from other radio wave sources and electromagnetic noise in general.

I hope this helps,
-GN