If you've already checked the mouse power-switch under the mouse is ON and a AA-AAA battery is inserted. This could be a possible issue with the automatic driver install after Plug and Play. The Green light will come and go off intermittently when the system is trying to detect the new USB device (mouse) during driver install.
Try these steps:
1. Check if computer is continuously connected to wireless or LAN connection
2. Remove all devices from USB ports of the computer and restart the computer
3. When the computer is ready plug the keyboard and mouse USB pieces. (Check if firewalls are disabled. You can turn it back on once everything work)
4. A dialog box will show the driver installation progress and the lights on keyboard and mouse will blink intermittently.
5. Once drivers are installed, test the keyboard and mouse they both should work.