Just to clarify all of this, when you are IP banned from a game or other location across the internet, it is done by banning your external IP. This is your unique identifier that is given to your internet line by your ISP. It goes as far as your modem. Once there, the cable company/internet services don't (generally) care what happens. It is sort of like your address at your home. An IP ban blocks this IP. You can see what it is from simply typing 'my ip' into Google. Google will tell you from what IP you are requesting information.
An internal IP, generally 192.168.x.x, is given to you by your router/modem depending on your setup. If your external IP is like your home address, you can think of the internal IP as your name on an envelope. The address allows mail to reach your house and then whoever gets the mail distributes it based on the name. All traffic going in and out of your location has your external IP but your router 'routes' the information using internal IPs. The difference from mail is that sites don't specify your internal IP when sending information back. It's just a simple analogy.
So, how this all relates. You get banned by external IP, that means the server won't send or receive information linked to your address. Resetting your internal IP via ipconfig /release and /renew does not change the external IP. Your external IP is assigned by your ISP. Turning off your modem and then turning it back on gives you a chance of being assigned a new external IP. This doesn't always work and so you may need to call and have it done manually. Many people will pay to have a static IP (one that won't change) for various reasons.
However, as has been mentioned, the best fix for this situation is to stop rage-quitting.