Unless you are using a router you can open a command prompt and type "ipconfig /release" without the quotes of course then hit enter wait a few minutes and type "ipconfig /renew" hit enter. you should have a different IP address. If not, keep doing this until you do. Your ISP sends out new addresses at specified intervals, just like The General mentioned. If a request went out for a new IP after you released yours, and before you tried to renew, they could get yours and you get a new one. Your computer tries to get the same address if it can first, then takes whatever it can get.
Now of course that doesn't mean they didn't block an entire range of addresses just to be sure you don't try that. If you have a router they blocked the IP of your router. Of course they may use MAC address blocking in which case you are screwed.