From your description of the computer locking after some period of time, either the user configured a password protected screen saver, or this is being pushed to the computers via GPO.
As far as the computer isn't allowing the admin logons to unlock it, you didn't mention if the same admin logon will work once you're at the logon screen after booting. It is entirely possible that these computers are not communicating with the DCs, so that admin logon (especially the one to unlock the workstation) aren't being authenticated by a DC. The first thing I'd check would be name resolution to be sure you're finding the DCs properly (pointing to the same DNS servers as the DCs), also try running netdiag.exe with the "/v" switch to report errors. It could be that the logons from the C-A-D screen (Ctrl-Alt-Del) are occurring via cached credentials (so try creating a new user in the domain, then try to logon to this box, if it can't, you're not seeing the domain).