If the DMS disk is broken (which it obviously is in the case), unless you have a hacked PhatBox you won't be able to replace the disk inside the cartridge with your own. If you still have contact with the original owner of the car, it would be worth seeing if they ever got round to hacking the box.
If not, you can still however buy original replacement disks, we still have a source!
The person I have in mind may make themselves known ... but I'll prod them anyway for you....