DHCP leases are reserved for a pre-determined time, they could be instant releases or could go for weeks, months, years. The marriage if you will is by the requesting devices Mac address, in this case the OP's router.
When the OP's router asks the ISP for an ip address, the ISP checks to see if there was a previous ip address assigned to the MAC address, if there is, it then it assigns the previously used ip address. This is where lease times come in. If the OP disconnected his router for a longer period than the reservation time the ISP uses, then when he re-attaches, he would then get a new ip address.
Most likely the OP got ip banned from a gaming or other type of server and is trying to get a new address so he can get back on. I know some routers allow you to mask a MAC address but I do not know if the OP's router has that capability.
You could call your isp and ask then to manually expire the lease......good luck though on getting through to the right person who actually understands and has the permission to do it.
troutspinner