It depends on your backup.
When you have ALL (files,folders + Dbase) it is easy.
Just for extra caution: make a new backup from the present (allthough may be faulty); just in case, not to loose anything.
Restoring up : supposing you have ALL in backup (like a 'backup mirror site')
(double check your config php (present) before you start and after (backupped old one) you finished for credentials)
Simply 'clear'your server (files) and empty dbase.
Upload all your (backup)files to the now empty server, and import the backupped dbase onto your sql server. ( same name)
As long as your credentials (paths + names) are still ok, your site should run out of the box..