In the Inbound and Outbound Servers Configuration of the Mail Connector there is only a connection to either Exchange or Domino.
There needs to be both Domino and Exchange server representation in the inbound and both Domino and Exchange server representation and in the outbound configurations otherwise the Mail Connector Service will not start.
In the Application event log of the Event viewer you will also see the following error
Service cannot be started. The handle is invalid.