All I did was went to online chat/support, they told me to D/L EADLM, the support dude asked for my e-mail I made my BC2 acc' on, gave them that, logged into EADM and pow, there it was ready to D/L no more DVD needed. No need to give over CD Keys or nada.
All they need is the e-mail you registerd already with and it'll automatically be updated in your EADLM, I also did it with my MoH (Even tho it's on Steam.)