I would be interested to know the following:
If you plug directly from modem -- PC, what are your address settings resolved to? IPv4, DHCP(status), DNS, Gateway.
If you take the router and disable all DHCP and routing functionality, and plug it from Modem -- LAN Router port (Not WAN) and plug the PC into the router LAN switch as well, what happens and what are addresses resolved as?
Model of your modem?