The \co-op directory on your largest drive contains the databases for all your project (that's the default during setup). Back up this folder and its contents. You might also want to back-up your project files, even though it is not strictly necessary.
If you don't want to back up your project files, make sure that your history is in good order--try selecting the earliest script and do Selection > Export Version. If it fails, some of the files in your history might not be recoverable and you won't be able to restore them based purely on history.
After you reinstall Code Co-op, copy the folders contained in the back-up \co-op folder to the new \co-op folder on your machine. Restore project files from the same backup using exactly the same paths as the original. To be on the safe side, launch Code Co-op and run Project > Repair for each project.
If you haven't backed up project files, Project > Repair will restore them using your project's history (this is why you have to be positive that your history is not corrupt). If your project is large, this may take a bit of time.