Lost my CD key for Battlefield Bad Company 2

Recently, I got  Battlefield: Bad Company 2 for PC on steam, and I couldn't make an EA account. I finally was able to make an EA account when I input a completely random email address. I was booted out of the game for no reason and then I realized that I didn't remember the email of the account at all, and this was the only account that had the Steam serial number. I tried and tried, but I just couldn't remember my email address. Suddenly, I remembered that I used to play Bad Company 2 on PS3 and I made an account then. I recovered the account as it was the email address of my most used email address and I tried to play the game. Then, I had to put in the email address. This is where it's gone downhill. I have no CD key as it's been inputted into and account I don't even remember, and I don't want to repurchase the game just for a serial key. Please, please help me with this problem.