You are talking about 2 hard drives, with two sets of permissions.
The permissions on your hard drive to be backed up...belong to a different system than the one on which the hard drive is now attached. I believe that, to change those permissions...you have to set new permissions from the new system.
I would try giving permissions to All Users for that drive...from the system it is currently installed on. That should allow you to move files to another drive.
An alternative that my accomplish the same, How to take ownership of a file or folder in Windows XP - http://support.microsoft.com/kb/308421
FWIW: That read-only box is insignificant, has nothing to do with permissions. That attribute is easily changed when necessary.http://support.microsoft.com/kb/326549
All of which forces me to ask...just how are you trying to backup this hard drive? The easiest course of action, IMO, would be to just clone the partition/drive.