Not that you're asking for suggestions, but....

My concern here would be that that computer is going to give up the ghost at some point and you aren't going to have a viable replacement. I'd look into running Win3.11 on VMWare. Or maybe even run the application in Wine.

But, if you're connecting to a mainframe and it's a Win3.11 program, is it just a 3270 terminal? If so, I've used x3270 many times and it works great. You can run it under Unix via X-Windows or on a curses-compatible terminal (xterm or the Linux console, for example), or under Windows inside cmd.exe or as its own window.