You should be able to install it from one of your Mac OS install disks, the one that says Applications.
If you downloaded it from the App Store, than you should be able to reinstall it once you delete the app. Just drag it from your Apps folder to the trashcan.
This should remove the app, though it will not delete loops, preferences and other configuration files. I'd try reinstalling it like this first, and if it doesen't work than I would reinstall after deleting everything that has to do with garageband inside
yourname/Library/Application Support/ (a folder named garageband)
and
yourname/Library/Preferences/ (like 3 files named com.apple.garageband.something)
Good luck!