It doesn't sound like this is your problem but the drive may be either read-only or encrypted? You can check by opening My Computer and right-clicking the drive to enter it's properties. Then look at the bottom and see if there are any boxes checked next to a Read-Only option. If not you may also check the folders leading up to the files by using the same method. If the drive or containing folders are "read only" you will be unable to change or overwrite them and possibly even unable to delete them.
The only other thing I can think to do would be to copy any files you DON'T want deleted on your compter's drive and then format the drive. To format the drive just right-click the drive again and instead of selecting Properties click on the Format option. It should bring up a fairly simple to use menu that you can format the drive with. This should refresh the drive and completely delete anything on it.
Hope it helps!