you are both right, and both wrong.
Your ISP (Comcast) assigns an IP address to your router, potentially a new address every time you reboot or turn on/off your router. This is your router's IP address. Your router assigns your PC an IP Address, probably something like 192.168.x.x. We call this a NAT (Network Address Translation) address.
Basically, it works like this. Comcast assigns you an IP address, let's say, 204.97.64.1 (just a number I made up). On your router you have a wireless laptop hooked in, your IPhone, your PS3, and a desktop PC. Your router will assign each of those individual devices it's own IP address...the laptop maybe 192.168.1.2, the IPhone 192.168.1.3, the PS3 192.168.1.4, and the desktop 192.168.1.5.
Each time one of those devices reaches out to the internet, through your router then through the Comcast connection, your router sends the information to Comcast as 204.97.64.1...and anything coming back from the internet to your devices sends that information to 204.97.64.1 (your router), which then figures out which device(s) it needs to go to, and sends it to the correct IP address(es).
So if you unplug the cable modem that attaches to your router, will that change the IP Address you're using on your PC? Probably not...that address is assigned by the router. However, the IP Address of the router *MAY* change, since the connection to Comcast was lost.
So, will rebooting your router and everything change your IP address on your PC? Maybe, maybe not, depending on how you have your router setup to give out IP addresses.
Will rebooting your router and everything change the IP address Comcast assigns to your router? Probably.
Hope this wasn't to complicated for you :)
Best Wishes,
Jeff