I have seen many having trouble restoring from Carbonite (and other backup products). If the backup was done while Thunderbird was running, the profile may be corrupt. I presume thunderbird was able to start with the profile restored, but some components failed? The addressbook can usually be restored with tools>import>import from a file and proceed from there until you get to a menu with 'sqlite' as an option. Then, select the file named abook.sqlite from your backup. For further assistance, please provide more detail on what is missing.