Frank pretty much explained it in his post. With dial-up, it's easy, as you'll automatically receive a new IP address each time you sign on, although you'll probably receive the same IP address multiple times within a period of time.

Since you have cable, it's a little more difficult, and depends on your cable company's settings. Usually you can unplug your cable modem for a half hour or so, then you'll be reassigned an IP address when you reconnect. However, if no one else in your area disconnected and reconnected their modem during that period, you my be assigned the same IP address. With other companies, such as Time Warner's Road Runner, you have to wait 24 hours before you'll be reassigned an IP address, but that's still iffy. And yet other companies lock your PC or cable modem to a specific IP address permanently. Thus, you can try unplugging your modem for a while, but if it doesn't work, you'll probably have to call your cable company, explain the situation, and ask for a new one.

Hope this helps,
John


P.S. You might want to check out BroadbandReports.com, which has threads concerning such topics. Just browse to the forum specific to your cable provider and see if there are any helpful tips/suggestions.