Looks like it was a weird/obscure firewall issue. The existing logon script was using NET USE commands to connect the users of the office to their shared drives, everyone was set up identically, and everyone was on Windows 7, but only one person was having problems with authentication. I changed a weird setting for just that user in Active Directory, and all of a sudden the error stopped and she was automatically connected when she logged on. I'll post what that setting was in case anyone here is curious or someone from elsewhere on the internet stumbles across this thread

Thanks for your help, guys!

Any advice on where to learn more about this side of things? Where do I start? Any online classes I could take?