If you use windows (2k or XP) start a command prompt. (Run as...: enter "cmd") Enter the command ipconfig /h - /h is help. It will give the help on any given command.
With ipconfig, you can config your ip - since in this case your ISP will assign you want we will just ask them to do so again.
Enter ipconfig /release.
A simple ipconfig command should show your ip was relased (it's 0.0.0.0) and no DNS ip availible.
Now enter ipconfig /renew.
It could take a while (5-15 secs) then a new ip will be assigned to you. Mind, that the ISP can change only the last couple of digits of the IPs he's giving out - so it the place that put a ban on you banned your entire ISP or bans everyone with the first digits in an IP (AOL for example) than you can't excape the ban this way.
Also some ISP don't have dynamic ip, so the same IP will always be assigned to you.
In that case use a proxy. (In layman terms it's like bounce point that masks your IP with its own.)
You can find the following page useful:
http://www.proxy4free.comLook for proxies that are *NOT* transparent.