You DON'T need LAN cards if both the machines already have a modem and they are connected through PABX system.
In Win98SE go to Start > Programs > Accessories > Communication > HyperTerminal. If it is not installed, you will have to install it from Add/Remove programs. This is one of the built in Win98SE application.
Here it will let you connect 2 machines via modem and telephone lines. One of the machine will have to
dial and the other one will have to
wait for call. You will then have to dial the extension number of the machine that is waiting. They both should be able to communicate with each other.
Try it out, it should work. I think even I will try this in my home and office setup. F.R.I.E.N.D.S., I must say that you are quite innovative

I never thought of this. This is something new but surely sounds very logical and must work.
But this will work only if you want to transfer files. You can't share other resources like CD-Writers or Printers. You will have to actually transfer files to the machine having those stuff. Also keep in mind that there may be dropped connections and file transfer is likely to be slow.