As pointed out, the flight was missed. But the key issue isn't why the flight was missed -- it is that the passenger earnestly TRIED to contact BA to indicate that the flight would be missed, but BA remained incommunicado -- thus permitting it to keep all the value of the ticket.
I would try to collect evidence from your cell phone's call history to demonstrate that you tried mightily to contact BA, but BA wouldn't answer the phone. Then write a polite letter to BA providing them with this evidence (possibly mentioning the traffic jam) and request whether they couldn't at least give you a refund in the amount that your ticket would have been worth if you had been able to notify BA that you were going to miss the flight.
I wouldn't hold my breath on a favorable answer, but by doing this you are giving BA the opportunity to take responsibility and "to do the right thing." Good luck!