|Sorry cohen but that's just not true.|
All you will accomplish doing that is to renew the same IP address in most cases. Most DHCP servers, by default, will keep giving the same address to the same client. Whoever administers the DHCP server could set it to use a different IP every time the lease expires, but most people don't as it really serves no purpose.
Also, as StuartS said, it doesn't do anything with external IP addresses. Those are assigned by your ISP and even if it's done using DHCP server, you're still likely to get the same IP address. Even if it's different, it'll still be in the same subnet which points right back to the same ISP.
With regard to what I said above about DHCP. My ISP gives me back the same IP all the time. I know of some ISP's that have it set to give out different IP's. This is an attempt to prevent clients setting up web serves at home on a "home" highspeed package. The ISP's want to charge them more $$$ each month for a "business" highspeed package. But there are ways around that too.........specifically using online proxies.
But, as StuartS mentioned earlier, using an online proxy doesn't prevent you from being tracked. The online proxy has a record of your real IP and your ISP has your personal information including your address. So, if you're doing some illegal and say the police want to find out who you are, they contact the proxy company and give them date/time/IP and then the proxy company gives them your real IP address.
Then the police use that information and go to your ISP. They give them the date/time/address and the ISP looks that info up and hands them your name and home address. Within minutes, the police are knocking on your door.
Anybody who thinks they can actually hide themselves on the internet is a fool.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.