When trying to add Domain users to Local Administrators group, you can only browse Local computer not the Domain. Here are the steps to trouble shoot the issue
1) Check if the Local System DNS is pointing to the correct DNS Settings as that of the Domain Controller Account
2) Try searching the user by giving the user account as DomainNameUser
3) Go to the Domain and See if the computer account is listed in the DomainComputers
4) If the computer is already there try to Rejoin the Computer to the Domain and Restart.
Most probably the issue is related to DNS Settings. Good Luck !!!!!!!!!!!!
