Did you install TS as a terminal server or this is just the TM that comme with the server. It it is the TM that comme with and you are on the DC it is normal to have administrator right because this TS is for administrative acces only. It is not meant to be a TS. A terminal server goes on a stand alone server not a DC.
their is a group in Windows 2003 that is call remote acces user I think. if you put your user their you’l be OK but you’l still have some applicaiton problemes. Terminal server is not design to run on a DC.