Since it works on other, identical, systems, it would seem to be something in the network setup. Have you physically moved the "bad" computer, to use the cable, and ports, used by one that works? When you do that, inspect the RJ45 connector, to be sure that it isn't damaged. Change the network card, for a known good one (if possible).
If that doesn't help, I think we need more information:
Exactly which version of OS/2 are you using?
Have you installed updates? Which ones?
What network software are you using? (SAMBA, NETBIOS over TCPIP, NETBIOS).
What network card(s) is (are) being used? What settings?
t may help to post CONFIG.SYS (be sure there are no passwords in it).