Follow this advice and you will find what you are looking for. Also I think you will recieve the same IP Address from whatsmyip.com if you plug your PC directly into the cable/DSL modem. You recieve the 192.168.*.* address usually cause a router assigns it via DHCP. Thus the reason for the said addressing scheme which you can easily tell by the Default Gateway of the router.
If you do an ipconfig /all look at the "DNS Server" there you will see it is not a 192.168.*.* IP but a 66.*.*.* as this is required to be able to surf internet websites. It basically "routes" all your "internal" network traffic to the "external" source that being your ISP.
I wasnt using 66. as a set DNS number just an example. The DNS IP Address your ISP provides is up to them and yep it is automatically assigned via your ISP. I was just distinguishing the difference to internal vs external.. internal most always being 192. or 10. now there is an exception where your DNS IP Address will be internal and that is if you are in a network env running a DNS server. Like here at work we have our DNS as a 10.6 that being a private internal address. I was using the 66. as a common Time Warner Road Runner ip address here in our small valley