Hard Drive Failed - Need to restore files with new computer

My C drive failed, and I need to restore my files.  I backed up the C drive with Norton 360 onto another drive regularly prior to the failure. Now I need to install the backup drive on my other computer that has Norton 360.  Will there be an issue trying to restore these files with Norton 360 on a different computer?  This computer has performed backups with Norton 360 regularly as well and has its own backup files associated with it as well.