First of all it all depends on what kind of router you are using..... not all routers have friendly internet setups, some have to be done via console.

SirDice was right, your ISP is the one assigning you an IP, you cant just up and choose one. But if that IP is blocked, there is a chance the whole range might be blocked, so having your ISP change the IP will do jack squat in that situation.

If you get more spacific about your internet connection, and what kind of connections you are trying to do there are other alternatives, like maybe a BNC? bouncing your traffic towards a server which will then relay it to the destination address and the incomming address would be that of the BNC.

good luck