@AllieKat5555 You can't transfer a game's installed files via flash drive; they specifically need to be reinstalled on the new computer.
What happens if you try to register the product keys that came with the discs in Origin? It's strange that they wouldn't have already been added to your Origin account, but if you can add them now, you can just download the packs rather than needing to use the discs.
If that doesn't work, you could always borrow a disc drive from a friend or family member and install the packs. If you then install a pack through Origin, that should remove the requirement to use a disc to play.
It's also a good idea to contact EA customer support and ask for help adding the packs to your account. Even though you can use the discs, having the packs in your account is more convenient and a backup in case you ever need it. When contacting support, it's a good idea to take a photo for each pack that shows the disc, its case, and insert with the product key easily readable; you can attach the photos when you submit your help request.
