A way to test whether your domain login credentials are working is via net use on the commandline like so:

c:\> net use \\<computername>\IPC$ /user:<domain>/<username> *

The * forces it to ask for your password. Otherwise, you can replace * with your password to do it all at once. Also, net use supports smartcard authentication, etc.

Thanks to Scott Morrison (a.k.a. "Plaid") for the tip!