Windows – Domain user not having admin rights on local machine

To get past the "There are currently no logon servers available to service the logon request" error you will need to connect to the VPN before attempting to log on.

Set up the VPN connection to have "Allow other people to use this connection" enabled (you may have to recreate the VPN connection entry to do this).

Once this is done, log out. Then, at the log on screen, click the "Switch User" button. A "Network logon" button should appear in the lower right corner (next to the power button).

You use this to make your VPN connection first, so that when you log in the remote logon server will be available to authorize you.

More info on this is available here.

I'm not sure why your domain user won't stick to the local administrators group, but it could be prevented by your work's Group Policies. Check out this SU question for more info on that possibility.