I have used the website to enter details for a flight whose miles haven't been credited to my account yet. Several weeks later I received a reject message, the reason given was "wrong ticket number".

This is odd. I have copied the ticket number from the boarding pass (I had sent myself an email with the BP), so how can it be wrong?

I can show them the boarding pass for the flight that I took, surely they can look up in their system whether I really took that flight. But how to contact them and have that conversation with them/send them the prove?