Some home network 101:
If you are using a home router, like a linksys, dlink, netgear, etc, there are two sets of IP addresses in play. The ISP will assign your router an IP address from its block. This is a real, routable IP address.
Your router will assign local, non-routable addresses to your pc, xbox, etc. Usually 192.168.1.x, where x is from 2 to 254.
The router masquerades all the local IP addresses behind the one assigned by the ISP. It has to, otherwise remote servers wouldn't be able to send info back to you; it has to go to a unique destination.
The remote server will know about the ISP IP address, but not usually the local one. There are circumstances they might, but I'll leave it at that.
So, the trick is getting a new IP out of the ISP. Bell uses a dynamic scheme, so rebooting the router will normally get you a new IP.
Not sure about Rogers.
When you get an new IP from the ISP, it might come from the same block. If the remote server is really mad, they might just ban your whole block of possible IP's.
Or I could be making all this up.