If you need to release your IP address, you ought to be able to go to run (or hit Windows Key + R), type cmd, and press enter.
Type:
ipconfig /release
That should release your address.
Then type:
ipconfig /renew
That should give you a new IP.
If you need an external IP from your ISP, you could likely unplug the connection bringing internet into your router. That will often ask for a new address as well.
Most ISP's seem to have long DHCP lease times, so even rebooting your modem rarely pulls a new address. Time-warner in my area only changes addresses once a year if even.