This probably doesn't have anything to do with logmein, as logmein doesn't care about Domains. It is more likely the PC isn't properly setup to communicate with it's domain controller. Check the domain controller's event viewer for any messages when you are trying to connect to it from that PC. Also check the PC's eventlogs for messages.
I suggest you move the Q to the Active Directory Zone or at least add it to that Zone to get more Active Directory specialists to answer.
