It greatly depends on what you ISP allows and what the device you call a "modem" actually is. In most cases the ISP will give you only a single routable IP address unless you pay them extra. This generally means you can only have a single router attached to a modem.
I am going to bet since you are not getting a IP address the ISP has some restriction. You are likely going to have to remove the current router and find a way to hook up your new one. The details on this will greatly depend on how your ISP has things done. The simplest case you can turn off the old one and hook up the new one, power cycle the modem and the router and it will work.
If they have it locked by mac address or they have PPPoE requirements then...