I'm not sure what your problem is now: are you still having the problem with the debugger message, or it has gone away by reinstalling GSX ?
If you inserted the Serial Number correctly, you should see a message "Do you want to activate GSX on this PC ?". If you don't see that message and FSX goes back to flying, it means you either entered the Serial wrong, or you entered it correctly, but with another product selected in the Addon Manager page.
Be sure you select Fsdreamteam and GSX on the Addon Manager before you click on the "Register Serial" button, and be sure you insert your Serial Number exactly as it is, don't confuse the letter "0" with the number "O", don't confuse upper case with lower case (it's usually all upper case), and insert everything, including hyphens. Basically, the Serial Number should be IDENTICAL to the one found in your purchase receipt.