So they have their network set up with manual IP addresses. When you enter the laptop's IP address on your machine, you prevent the laptop from being able to access the network, since each address can only be used by one computer. They could have your MAC address and blocked it to prevent you from stealing IP addresses. There are ways to spoof MAC addresses, but let me warn you, you already obtained the wifi password through questionable means and have found that IT has configured the network with manual addresses. These are clear signs that you are not allowed to connect your devices to the network. Proceeding with further attempts to bypass the school's security would not be viewed favorably by the network administrators.
Your teachers may say the internet is for your use, but the network administrators have put these protections in place because unauthorized access to the network can cause problems for all computers on the network. Don't make their job more difficult by breaking through their protections.