If you bought it off steam then it shouldn't ask for a CD-Key. In fact it shouldn't at all because Batman AA CD-Keys aren't accepted on Steam as seen here https://support.steampowered.com/kb_article.php?ref=7480-wusf-3601
If you did buy the game off Steam on the account you're currently using, and the problem is still occurring then I'd advise you to contact Steam for help.
If the game came with an NVIDIA Graphics Card then the code that you received when purchasing it is NOT a serial number. To receive your serial number (after you have downloaded and install 'Batman: Arkham Asylum'), do the following:
Right-click 'Batman: Arkham Asylum'
Click "Show Serial"
This is the serial number for 'Batman: Arkham Asylum'. Use this key to activate your game.