One possible problem I see is that it looks like you have your DNS servers designated in your IPv4 properties rather than letting your router handle the task? It may help to remove those DNS entries and let the router handle DNS. You can designate your DNS servers in the routers set up page. Most routers will show the DNS as the default gateway which points back to the router for the DNS servers.
I also noticed that your subnet mask isn't normal. With your default gateway of 192.168.0.1 the subnet mask should be 255.255.255 not 255.255.255.192, the 192 part may be left over from your schools network settings and may be causing problems.
If you need to connect to two different subnets you need to define the two different networks by going into your advanced TCP/ip settings and add the different subnets and IP's to the list "picture below"
I also noticed that you have extra tunnel adaptors in your ipconfig /all, those will sometimes cause problems with your network and can be delated by going into device manager, select the "view" option then choose "show hidden devices" at which point you will see them all and they can be delated.
Do not disable IPv6!