This is definitely something that needs investigating. To me, and I can only surmise, it sounds like a situation that heppens infrequently:
1. Between checking-in and reaching the Boarding Gate, the e-ticket has become disassociated by the BA Res system due to no payment having been made by the Travel Agent.
2. Reservations attempt to contact the Agent for payment with no success.
3. Passenger offloaded.
David Johnson 6 may not be entirely correct. If the airline offloaded you in error, then you will be entitled to seek compensation from the airline.
If the Travel Agent had not paid the airline, then the liability for compensation will lie with the Travel Agent, unless you or your employer had failed to provide payment to the Travel Agent.
So, after you have done your investigations, please let us know what happened.