British Airways comair made us pay full price for a flight even though they had a system error

Yesterday myself and friend received a email from @britishairways @kalula to checkin online but it unfortunately did not work . Cape Town International Airport This morning our flight was at 6:45 we arrived at the self checkin counters at 5:50 and tried it didn't want to let us in then we went to checkin at counter 76. A very short, coloured, female was just rude we told her the situation and what happend keep in mind it was 5:55 and she told us with other passengers standing in the que oh you missed the flight go pay for another one. This is not fair as firstly @britishairways @kalula sent us a email to checkin work. Then the link never worked. When went to @britishairways help desk and then two ladies over there then assured us that we were not the first to complain about the self checkin machines, and online email links not working. We had to pay full price for another flight. Keep in mind we are both students so this is financially draining. @britishairways staff at the checkin counter 76 is so rude and not helpful at all. They have no way of communicating with passengers.