I am also waiting for a reply from customer support. Have the invalid serial number problem.
However, I only have 1 account and the serial bound to it was a KA50 and not an A10C serial. After unbinding it from the page / account I was still not able to play on multiplayer after re-registering / activating my local game. Either my key is a KA50 key or somehow my key and some KA50 key got switched during the registration process. Maybe somebody has the same problem who bought KA50 and now has a A10C activation?
I was getting help from 5 friends who also own this game and we all were not able to figure out what could be the problem. It was really unusual for me to have that KA50 serial under myserials...
I can play DCS A10C in SP as it is activated in DCS World.
And yes, I read the FAQ and Hot Issues section.
I would appreciate any help.