I had the same problem,, I worked on it for hours and hours.. finally I gave up and restored my PC to the time before I had un-installed the mouse in the first place. That being said. I had been all through my registry and control panel etc.. there was one service that was blown away when I did the un-install that came back when I did the system re-install. If you go to your services.msc in the start menu, there should be a service called Bluetooth Support Service. This is in addition to the Bluetooth Service. The path to the executable is C:\windows\system32\svchost.exe -k bthsvcs It's dependencies are Remote Procedure Call (RPC), DCOM Server Process Launcher and RPC Endpoint Mapper.
Another thing you might try is to re-install your mouse drivers manually. They are located at C:\windows\system32\drivers\mouclass.sys and mouhid.sys
File Version 6.1.600.16385 (win7_rtm.090713-1255)