Stupid question but is the base-station plugged into a functional USB port?
Ensure that it does otherwise even if your mouse communicates with the base, it will not transmit any tracking information to your computer and therefore will not function.
Alternatively, ensure that the base-station and the mouse are synched. If they are not, you need to get it done. There are tools on the Logitech website to allow you to do this.
http://www.logitech.com/index.cfm/support_downloads/&cl=us,en