If the router is set up correctly then you don't need the old modem. Disconnect it and uninstall any speedtouch software.
The router settings for your ISP are set up when you run the Zyxel Set Up wizard. Check by typing click here. into your browser and it should bring up the control panel for the router. Check ADSL settings here. (Think this is the address but may be different for your model Which do you have?)
If you cannot connect to the router then maybe a firewall issue. Disable the firewall temporarily and try again to test.