This depends. When you go into the TCP/IP settings there is a Renew IP Address button. If you click it you may get a new one, you may not. You could select the pull-down that says "DHCP and tell it "Off", click OK and Apply, then go back in and select DHCP, OK and Apply and see if you get a new one.
Chances are your router has associated an IP address with your MAC of hardware address and will automatically give you that one. If thats the case you need to go into your router and see if you can edit its DHCP table and delete the entry for your computer. If you can do this do it with your computer off, just in case it wants to pick it back up again.
A last resort would be to reset your router to clear its DHCP table.
Just spit balling some ideas here.