You will have to re-join the domain before you can have access to it. This means that you will have to have the correct permissions on the domain to be able to add a compter to said domain
If I understand correctly, Tvoss217 could not re-join the domain because he/she doesn’t even know what the domain name was, and that’s what he/she is trying to find.
I think you could have a look at the following files in the local machine:
<b><WINDOWS_DIRECTORY>\security\logs\winlogon.log</b>: I think you could find the domain name here, if some domain policy was applied to the machine sometime. Look for some text including “GPO”.
<b><WINDOWS_DIRECTORY>\debug\NetSetup.log</b>: Look for “NetpCheckDomainNameIsValid”, a function that is called by the OS to verify domain names.]