To correct this, you will have to go into File -> Security -> User Security (as you are attempting to do), and make sure the "Don't prompt for a password from other Notes programs" is enabled.
(As well as the other steps listed in
http://publib-b.boulder.ibm.com/lotus/c2398580.nsf/b3266a3c17f9bb7085256b870069c0a9/fda328692346dc1f65257607002ecb59?OpenDocument).
So the first order of business before you can do that is to fix the ID file, because clearly there are problems there. Try right-clicking on the ID file itself, selecting Properties, and making sure the Read Only box is not ticked. If the file itself is somehow corrupt, do you have another copy saved somewhere you can replace it with?
Alternately, if you don't expressly need to use the admin ID file, you could use the Server ID instead.