You're router isn't pulling a new address when you access wifi on your phone. This is what happens.
You turn on your router. It sends a request for IP configuration. Your ISP fulfills that request and sends back configuration data. This is called DHCP (dynamic host configuration protocol).
THEN your router sets itself up has a DHCP server. When your computer, your phone, printer, etc. asks for an IP... your router supplies that information. When you browse with it, your router changes the IP address of all the traffic to it's own IP address (generically, specifically it changes the IP and tracks the request by port number, which it associates with the request from the IP address from whatever the request came from.. aka NAT (network address translation)).
Changing the address on your phone will DO NOTHING to avoid that ban if the systems admin who banned you is even halfway decent. You could attempt to change your routers IP, but thats the fun thing with DHCP. It leases you that address for x length of time. As long as that time hasn't passed, it will assign you the exact same IP address. When that time is 1/2 up, your system renews the lease if it can reach the server. You'd first have to determine how long the lease is (something you can't do from most factory routers), and then shut off the router for that length of time (disabling your internet for that period as well, usually the lease is 7 or 30 days), and HOPE that after your lease expires, someone else, who has no active lease, requests an IP address before you do. This is basically someone who just had the service activated, most everyone else will already have a lease. Getting that IP address to change is a pain. If you attempt to set it manually, you will, eventually, cause an IP address conflict on the network and your provider will just shut you off to keep the problems down. They can tell who is causing the problem pretty easily. It would take me a grand total of about 5 minutes to discover the culprit on my networks. That includes logging in.
In other words.. it's not easy, what you want to do wont work, and quit being a duche on the different forums and getting yourself banned.