If you really want to salvage the original game, you could put the hard drive in the new computer, or get a hard drive disk enclosure to also turn that hard drive into an external hard drive. Wether you want to salvage the old one or not, I do say that the external hard drive idea may give you more storage space. Heck, it even would still have the OS and license the old one has.
Just be sure to touch metal or wear anti-static stuff if you try to extract the hard drive (also make sure the battery is disconnected), as static electricity can permanently damage components. I would offer to do the whole extraction part if that feels like a lot of work, but I think we'd both be a little uncomfortable with sending or receiving the broken laptop.