You will need a Router that supports RS-232 (serial port) ... not that easy to find.
A simpler solution is to set-up a network using a 'switch' and ICS (internet connection sharing) in the PC with the dial-up modem ... that, of course, has its problems too.
There are several reasons ... you can't get 'broadband' for some reason or another, you cannot afford broadband or you need an alternative to broadband for back-up if broadband fails.