You SHOULD have codes for those disks, ie even on disk copies, there is a drm that requires entering in a game code. You SHOULD be able to use said code to unlock it on EA app or as it used to be called Origin app. I thought when DAI came out it also required Origin app to be installed, and thus entering in said code unlocked the game on your EA account, and thus to install the game if that is true would simply require you to log into your EA account on the new EA app, and load your library.
So If my memory is correct, you should have already unlocked the game on your EA account from originally installing the game and authorizing it to play and only now need to log into your account and download it again. If my memory is wrong, then look for the game code and see if you can use it to unlock the game on EA or steam platform....may have some issues due to being an original game and pretty much every copy available now is the GOTY copy with all DLC.
Another option is to look for DAI to be on sale and buy it again on your platform of choice, I have seen the game available for under 10 dollars US many times.
(CM edit updated title)
