All depends on how you "lost" your hard-drive. If you can find your old profile, If your backup really is corrupted or directories are just pointing wrongly.

I have re-installed my start-up backup system... I have no link to my old system... just whatever is on my server for things like my email and contact list. When I re-installed T-bird, I didn't know how to answer questions to re-connect with my original account. Can I start over again? If so, what are the right answers to get my address book and local folders back?

If you didn't format your harddrive Open explorer and type: %appdata%\Thunderbird\profiles in the address-field. Can you see more than one directory with random names?

Don't start over, you end up just like now. You have a backup if it wasn't really corrupt it would restore but under old profiles name. It would contain all your accounts, mail and settings.