Using a dial up connection with a broadband router is unlikely to work here unless there is a setting in the router configuration to change its role from a gateway to a router. The distinction is in how the router acts in distributing an internet connection.

A better scenario would be to use your dial up connection on whichever machine will serve as the gateway. Configure the gateway, enabling ICS (Internet Connection Sharing). Connect the other computer(the client) via crossover CAT5 cable to the gateway computer. Set the clients IP configuration to be obtained automatically.