I'm actually having the exact same problem as the OP. I have followed your suggestion but find the exact same issue as the OP. It shows my Transaction history, with the Transaction ID, date of purchase, version bought, etc. However, it does not show the serial number anywhere.
First thing I checked before finding this thread was the sticky at the top of this forum. http://forums.eagle.ru/showthread.php?t=57556
According to the sticky, that's what I should see.
But, when I check my tranactions in the payment section it does not show any of the orange texts.
Still trying to find my serial number so I can reactivate. I recently built a new PC and I've been struggling with this issue off and on for the last couple of weeks.