I bought a replacement mouse for the previous Microsoft Compact Optical Mouse 500 v2.0 that I had because I like the model. The first mouse I had was plugged into one of the USB ports on the right side of my laptop and it worked perfectly fine. Yesterday I began using the replacement mouse (remember, they're the same exact model) and it wouldn't connect in either of the USB ports on the right side of my laptop. Fortunately it works when plugged into the USB ports on the left side but the cord is so short that is very difficult to use. It also lies completely across over my keyboard making for an annoying and uncomfortable usage. The only thing that I've done to my laptop recently is clean the dust from the fans. My external HDD worked fine when I plugged it into both USB ports on the right side so I don't know what the problem is.
MS used to host a file called msicuu2.exe or Microsoft Install Cleanup Utility. It was originally written to remove stuck MS Office softwares and had conflicts with other things so I think they have removed it. It would find stuck things similar to what you are mentioning if they were installed using Windows Installer. I had tons of success with it and never ran into the bad stuff. If you can find it.... it may be worth a shot as it would find stuff that wouldnt even show up in Control Panel/Add-Remove. If you can't find it or don't trust the site, msg me and I will email it to you.