Obtaining Serial number from older purchases

I bought this game as well as Sims Medieval in 2011 and played them often on my laptop. However, I bought a new computer in January as my laptop stopped working very well.

I would like to be able to access the full functionality of the games I purchased but now lack the serial numbers as I do not have the original e-mails with them from 2011 any longer as I try not to hold onto e-mails for years at a time. I would like to be able to use the games to their full potential on my PC though. It's evident by my Origin account that I purchased both games, however, it doesn't show a serial key under the products that I've noticed. If I've missed this, I apologize, but I'd like to have the serial numbers if possible. They must be on record somewhere.

The only thing available to me via Origin is the product key, which doesn't work.

Thank you for your time.