If on a 2003 server the remote desktop service (RDP) is not working, check the following:
1. Any firewall (windows or third party) is not blocking the port TCP 3389
2. Issue command "netstat -an", search search the output for the TCP port 3389. If it there, try to telnet to the port 3389
3. Terminal service (TermService) is running (it cannot be stopped or started though, that's impossible by design). Check also the "Terminal Services Manager".
4. HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Terminal Server\fDenyTSConnections must be (0) to accept connections.
5. Try to delete and then recreate the rdp connection under "Terminal Services Configuration" (Reboot the server on each step). Bind it to a valid network adapter.
6. The "Enable Remote Desktop" is checked in the Remote tab of the "System" item of the Control Panel
7. Restart the server once more time.