With the PC plugged into router, and router into modem, you say you can ping from the router admin page?
If so, you should have full connectivity, ie PC has an internal IP address (it can connect to router admin page) and router has an NTL external IP (it can ping
www.bbc.co.uk).
What does 'ipconfig /all' at DOS prompt show?
Can you browse to 192.168.100.1 - the default admin page for the cable modem? That would confirm whether the router is passing taffic through from internal network to WAN port.