I am having trouble deleting old Vista backups off of my network backup location.

These files are no longer accessible nor needed.

Does anyone know of a way to eliminate thses files and folders?

Thanks in advance

From Microsoft:


How do I delete a backup that I created using the Back Up Files wizard?


If your backups are saved to CDs or DVDs, you can discard discs containing earlier backups, but make sure that you keep the most recent backup of your files. If your backups are saved to an internal or external hard disk, you can delete a backup by following these steps:


1. Open the location where the backup is saved.

For example, if you backed up your files to an external hard disk labeled "E," connect the external hard disk to your computer, and then open drive E.
2. Right-click the folder containing the backup you want to delete, and then click Delete.
Notes

* Backups are saved in this format: <backup location>\<computer name>\Backup Set <year-month-day> <time>. For example, if your computer name is Computer, your backup location is E, and you backed up on April 2, 2006 at 16:32:00, that backup would be located in E:\Computer\Backup Set 2006-02-04 163200. You would right-click the folder named Backup Set 2006-02-04 163200 to delete that backup.
* When you make a full backup, a backup folder is created and labeled with the date for that day. As you add updates, that date stays the same, but your backup is not out of date. The next time you make a full backup, a new backup folder is created and labeled with the date for that day, and any updates are then added to that new folder. You should not delete the current backup folder.

I have tried to delete these files several different ways, none will work since it says I need to have permission to perform this action.

I only have one account, user, administrator on the system and am signed in as administrator with admin privileges.

Then you have lost the ownership to these files and must retake control over them in order to delete them.

Change the permissions and take ownership of your files and folders | Windows Vista for Beginners