Edit: The issue at this point is that a regular user is granted access to the registry and there is no prompt for administrative credentials whatsoever. Prior to changing permissions (See Scott's answer below) even an admin received an "Access Denied" error. After changing permissions any user can access regedit.
How do I get the system to prompt for admin credentials and then use them to run?
When executing "regedit" from either the "run" prompt or the command prompt I receive access denied error messages.
On the other systems on my network the user is prompted for administrative credentials instead of receiving an error. On this system there is no prompt. From the "Run" prompt I receive the error after typing Regedit:
"Windows cannot access the specified device, path, or file. You may not have the appropriate permission to access the item"
From the command prompt I receive an error that simply states "Access denied".
If I escalate the command prompt (run it as an administrator) then regedit runs just fine. The problem is that the lack of a prompt for credentials might be related to other issues on the system.
As a note, using "mstsc" to attempt a remote desktop connection also causes this same problem. More "run" commands may do the same, though I have not tested this.
Is there a setting that forces a prompt instead of just giving an error?