Can the computer in your dormitory still surf the Internet? I don't know what kind of network mode your school is. If the school has broadband access, there is no need to set up ip or anything. If their dormitory is connected with their own network cable, of course, your computer can't directly access their dormitory. Set up the LAN ip, the small lock on the local connection has nothing to do with this, don't worry.

My suggestion: check whether there is something wrong with the network card of your machine. If you ping 127.0.0. 1, your machine will be fine.

(It is absolutely excluded that the school network management is bound to the mac, which is not considered)