I got scammed by EA

About 5hours ago i bought bad company 2 through ea play, the game appeared in my steam account (but not on my EA account) i have connected to my EA account, downloaded the game and when i opened it and clicked on the server browser the game asked me for a cd key that i do not have. Steam automatically says i need to contact the original key provider (EA Play in this case) and when I contacted them I had very long conversations with multiple EA HELP employees all of whom stated that they cant help me (even after i provided the wanted proof of purchasing the game) and that my only chance is to either contact steam support or refund the game on steam.

TLDR: bought bfbc2, game asked for cd key, EA told me they cant give it to me even though i showed them the receipt. So now i am 4 dollars short and without a playable game