Without going into too much detail, pretty much everything in Active Directory has a GUID, which by definition won't be the same after a re-install. The GUID of your domain and computer object will not match, so even with the same "human friendly" names you will be unable to logon.
If you need to get Active Directory running again so all users and computers that existed on the dead server come back, you will need to do an Active Directory restoration. This is also why you have more than one Domain Controller.
If you simply need data off the computer you have, boot into a live CD of some description and pull files off that way.