"....the modem has a USB connection"
Then you cannot use it with a router without a USB port. As USB is not a network interface, very few routers have it and it is less likely to work. Cable/DSL routers are intended to receive PPP over Ethernet, which cable services use. Your modem is, by the sound of it, an ADSL modem. ADSL uses PPP over ATM in the UK.
"...a 'twisted pair cable ', Is this a RJ-45 cable?"