I suspect the problem is not actually with the IP address allocated by your ISP, but the address that your PC has and which should be allocated to it by the router.
Previously, when your PC connected directly to the ISP, it got its address from the ISP. Now that you have installed a router, it is the router which connects to the ISP and gets your "public" IP address. The router in turn allocates LAN IP addresses usually in a 192.168.x.x range to all computers connected to it.
If you haven't configured the router, and your PC cannot get its IP address from the router's DHCP server, Windows will default to allocating an address in the "169.254" range which will give the Limited or No Connectivity indication and you won't have network/internet access.
To configure the router, connect initially with an ethernet cable and type the router's IP address into your web browser. If your Local Area Connection doesn't have a valid "192.168" address, give it a fixed address in the same subnet as the router. If the router's address is 192.168.1.1 then give the PC the address 192.168.1.2 and Subnet Mask 255.255.255.0