The first question is how did you do the backup? Was it as a complete back up of the disk or did you separate windows from Linux?
Assuming you just did one backup then restoring should just re-instate your machine to how it was prior to the backup.
IMHO Linux should always be installed on three partitions, the system(/), swap and home. In this way if something like this happens then it only the system (/) that would need to be re-installed. Additional programmes that you have added would need to be re-installed as well but all your settings are in the home partition. When dual booting between windows and linux I always have a data partition formatted to NTFS on which I keep all my information. This allows windows and linux to access it as windows does not recognise the linux partitions.
If you are sucessful in reinstalling your backup then I suggest you use luckybackup to backup your home file and I think you should be able to install it to a new home partition, you would how-ever have to point fstab to the new location. I have not tried this but think it would work.
Edit: Found this article which should assist. http://www.howtogeek.com/116742/how-to- ... ng-ubuntu/