DOS Program reconstruction

A client of ours uses a legacy DOS program Contractors Management Systems for estimating and has been running it on an old 386 computer (against my advice). We were able to extract the bulk of the data and the program and have the dongle that was required for the program to run, but are having trouble getting the program to run on another machine. The vendor is no longer in business. We have the original 5.25" disks, but they have demagnetized through time. Because of the possibility of some program files being damaged, we may need to look at importing the data into another program. We are open to either importing data into another program or repairing the existing program. (Preferably repairing the existing program). Data has been saved in .txt files and program files are in .dat, .bat, .com, and .exe (some .as1, .as2, .as3 and .pwd as well) Time is of the essence with this project. I have NO idea what kind of budget we need for this, so if I need to adjust I can.