The thing is that the University folder still exsists and it's fine and whole.
Are you sure that it's
completely whole? Make sure you have a file called Sims2EP1.exe in your Program Files/EA GAMES/The Sims 2 University/TSBin folder. Sometimes an EP's executable file will mysteriously disappear, which results in an error message saying that the EP is not installed.
If the executable is missing, you should be able to copy and paste it off of your disc. No uninstalling/reinstalling required!