You might be better off running Windows on the machines and running the program through
DOSBox. It's a DOS emulator that pretty much has 100% emulated compatibility. It emulates older hardware on your newer hardware, so that might take care of your problem.
If you can't afford to put Windows on them, put some kind of free Linux, like
Ubuntu. DOSBox has a Linux version, too.
The main reason people use DOSBox is for old DOS games, but it will run anything DOS.
And your original problem is probably because you "imaged" your DOS set up from one computer to another one that had totally different hardware. You can't do that. Just use DOSBox.