Well, you should've removed it through Add/Remove programs. JJ2 thought it was installed because its registry entries had not been removed, and I'm guessing the registry settings are causing your problem.

To get off to a clean start, you'll need to remove your JJ2 folder once again. Then, go to Start->Run, and type in regedit

Be careful and follow these instructions, and don't touch anything else in the registry.

Go to HKEY_LOCAL_MACHINE->Software->Epic Megagames. Remove all JJ2 entries.
Go to HKEY_CURRENT_USER->Software->Epic Megagames. Remove all JJ2 entries.

Now you should be able to install the game the proper way.