Pretty much all networking problems with your machine can be fixed by running the batch file below other than defining different subnets.
From what I'm seeing here the router or it's settings are part of the problem, in that the subnet is different than the one at the school. When connecting to different subnets with the same adaptor you usually need to define or list the two different subnets and default gateways in the advanced TCP/ip properties window.
The picture below should make it clear where you need to enter the two different subnets but you will need the subnet and default gateway from the school first.
The batch file will be easier than running system restore and may be worth a try.
This will will reset winsock, reset the TCP/IP stack and release renew your IP.