|"I downloaded the binary file to a floppy disk. Have I done that properly?"|
No. You have to download the file to a hard drive and make a bootable reference disk on the floppy. Running the executable should be self-explanatory. I remember somewhere (been a long time ago) that it was best to do this on a machine running DOS/Win3.1 (something about how the floppy disks were formatted). That may have been for the .ADF files, so I'm not certain (been a long, long time since I've worked on a PS/2).
"Pulling out the floppy drive I discovered that the cord connecting the floppy drive to the board had the first wire broke."
If memory serves (and it may not), a standard floppy cable should suffice. Make sure it's "broke" and not "intentionally cut", which would indicate something particular about that floppy configuration. Do a Google search on "floppy drive cable" and you should be able to find who has them.
Some links that may assist with the machine:
"The floppy drive also does not work."
You'll have to get that working to ever set up the configuration on the machine.
Also, don't be terribly surprised if the hard-drive doesn't work either, you're working with a machine that's probably over 20-years old.
"Channeling the spirit of jboy..."