Have a look at DOSBox - it runs on XP or Vista, but emulates DOS. Its primary purpose in life is to emulate DOS for old games, so it’s possibly going to have problems with non-gaming activities like printing and getting onto a network.
Has he tried running it from a command prompt? If this is just a command line program (non-GUI), it will (probably) work. Even some graphical programs will work. Failing that, find the program executable’s icon in explorer, right-click on it, select properties, go to the Compatibility tab, and try some of those options. If those fail, then go and get DOSBox, like gotpasswords suggested.
Every version of Windows has come with a command-line shell that runs DOS programs. If you’re not doing anything fancy with sound and graphics, this should be sufficient for your needs.
Based on your description it’s a little confusing exactly what type of program this is. If the name ends with .COM or .EXE you may just be able to copy the file to the new computer and just click on the icon directly, without using the command prompt. However, printing may be a problem.