I don’t have the wallet.dat files as I never generated that back on my old computer
It’s not clear to me what you mean by this. There is only one wallet.dat file (plus any backups for safety). It starts empty when Bitcoin QT (currently Bitcoin Core) first runs, and after that the wallet.dat file accumulates your Bitcoin transactions which determine its bitcoin balance. The transactions are stored in the blockchain, which Bitcoin QT initially downloads from peers on the internet and then subsequently updates whenever it is running.
It seems that you cannot boot from the old drive. Can you access it at all to see and possibly recover files from it?