First, are you talking about your internal IP address or your external one?
Your internal IP address is the one that is given to your specific computer by your router, and only works inside your house. It most likely starts with 192.168.x.x
The internal IP can't be seen on the Internet and is only used inside your own home network so your router can keep track of which computer is which.
The ipconfig command works on the internal IP and only the internal IP. It doesn't do anything for your external.
Your external IP is the one that your entire house uses to represent itself on the Internet. This is the address that everyone online sees, and technically it is the IP address of your router (because in reality your router is the only device in your house that's actually on the Internet, all the other devices just relay data to the router in order to get stuff from online). Your external address is given to your router by your Internet Service Provider.
Most house subscribers have what's called a dynamic IP address, which means if you wait long enough your ISP will change the address on their own. If you don't want to wait though there are a few things you can do to change your address.
1. You can try unplugging the router, waiting five minutes, and plugging it back in. This forces the router to ask your ISP for a new address. However, depending on how your ISP is configured, they may just hand you back the exact same address you had before. In which case, go to step 2.
2. You can try releasing/renewing your IP. You already tried this on your computer, but like I said the ipconfig command only works on your internal address, and we're trying to change your external. Remember your external address is actually the address of your router, so you will have to get into your router settings in order to release/renew it. Unfortunately, every router is programmed differently so I can't give you more specific instructions. If releasing/renewing the IP inside your router didn't work, or you're not comfortable going into your router settings, then go to step 3.
3. Call your ISP, and tell them to renew the IP on their end. After they do so, reboot your router again and you should have a new address.
Keep in mind that even though your external address changed your internal address will remain the same so your computer will still report an address of 192.168.x.x. If you want to see what your external address is, use a website like whatismyip.org
You can also use a proxy service, which doesn't change your IP address but relays your data through someone else's so that it appears you're using a new address to everyone else online.
Hope that was enough info for you and not too confusing. Best of luck!