Thanks.
So basically you just back up the following files from your Firefox profile:
places.sqlite (bookmarks)
key3.db (key database for passwords)
signons.sqlite (passwords)
cookies.sqlite (cookies)
Remove Firefox along with the profile, download and reinstall a fresh copy of Firefox, then run Firefox for the first time (creating a fresh profile).
Then it's just a matter of copying the backed up files into the new profile, replacing those already there.