Exchange server in an AD backup/restore scenario

JudeCP From an architecture point of view it is very unusual to have only one DC in an environment, no matter how small the environment is. It's okay to have one DC for LAB environment where you do not care to recover anything.

If you had two DCs in your domain, in this case you just could have built a new DC in the existing domain. Now that you have lost your only DC of the domain and the backup you have is older than 30 days, you do not have any other choice! I would restore the DC and try rebooting the Exchange servers first. If still they are out of the domain, you have to dis-join and rejoin them again. Even if your Exchange severs start talking to the domain from windows perspective, you may face various issues with exchange. Good luck!