Apparently you were using OTFE (On The Fly Encryption: an encrypted message base) with your previous install. The addrbook.eni is the encrypted form of the addrbook.ini, however it doesn't contain any addresses, it contains the names of the actual address books you were using.
Your real address books can have any name, but have the .ebd extension (.abd when you don't use OTFE)

When you've still got your .ebd files the addresses are retrievable. Not as easily as you might think though, that's because you were using OTFE.

Basically you need to install TB anew, choose to use OTFE, use the same master password as your previous install and now you can import from the .ebd files.

When you've got a backup from your old install (as in created by TB), then you can restore it as backups are unencrypted (unless you select to encrypt it), note that restoring a backup means that you over write existing messages, accounts, etc, so you'll loose your current data.

I hope this helps.

And next time you install a new version of TB, just install it on top of the previous version, that way it'll use the same settings, etc as the older config. So don't uninstall the previous version.