You would use Migration Assistant to migrate the old "you" from your backup.
If your issue was user specific all along, you may reintroduce the issue by migrating. If you fear it was user specific, you should log into Root and manually navigate into your backups.backupdb folder and find the desired apps, docs, music, movies, and pictures, and then copy them to the desired and respective locations of the volume, but you will have to address the permissions using "Apply to Enclosed Items" to make sure they will open, edit, and save correctly, depending on the contents that you bring over. Permissions can be a pain sometimes.