That looks like good news jaime41.
It would appear that you can see all your old backup files here if you need them. Now let us tidy up, and set up a new and usable backup set.
First delete all the files in the new N360_BACKUP directory on your Z drive. Leave the original Norton Backup files where they have been all along. If you need to recover anything from them you can always copy them back to the new N360_BACKUP folder and access them but for now keeping that folder clear will make things tidier.
Once you have cleared out the files have another look at the restore possibilities in N360. This time there should be nothing visible. If there is, post a screen shot and try and work out where the physical file is. If there is nothing we can proceed with creating a new backup set.
Go to Manage Backup and "Delete Backup set" for any sets that you do not plan to use. It will not let you delete the last one whatever that is, but do not worry. If you are unhappy with the name of the remaining backup set you can always select the Rename option. Then with the name of the set you wish to use as your normal backup in the window on the Manage Backups screen, select the "Where" tab, choose the Z drive and, I would recommend, make sure that the "Verify backups" box is ticked. The go to the "When" tab and choose when you would like the backup to run. Automatic is probably the best for you.
Then go to the "What" tab and select what you want backed up. You seem comfortable with this so I will not go into great detail but I will just put in two pointers. If you specifically include a folder then I believe that all the files in that folder (except probably any files that Norton thinks are encrypted) will be backed up. However if you use the "My Documents" option on the left and the file types selection on the right, Norton will only backup files with extensions that match the extensions in its current file type list. So in this latter case you may want to check that you are not using any unusual extensions. If you are then you would need to add them manually.
Once you have set the Where, When and What - save the settings.
Select Preview and it will tell you how many files and how much space the backup should take. If this looks odd come back and explain what you see and why it is odd. If it looks reasonable then manually run the backup from the Manage Backups screen. This may take a long time depending on how many files you have chosen. So you may want to run it overnight or when you do not need to use the machine. Future backups should be incremental and only take a fraction of the time.
Hopefully you will get a report of a successful backup. Once you have got this go to the Restore option and look to see if you could restore some of your files. If this looks as if it will work then all seems good and our work is done! :-)
Two final thoughts.
1.- I normally have two separate backup sets, one that runs automatically and one that I run manually. This means that if for any reason one gets corrupted I still have the other. You may like to consider such an option.
2.- Once you have set up your new backup and gained confidence that it is working you could delete your old backup files (the ones that cannot be recovered without moving them to the new N360_BACKUP folder) to save space and avoid clutter. However given the size of the disk this does not seem to be a pressing need.
So hopefully all is now sorted but it would be good if you could report back after you have done the above and let us know what actually happened. ;-)
Good luck.