I use VNC on a regualr basis to update my other computer without actually having to go to and what not. So here's what you migth need to do.
On your home computer, run VNS SERVER. Then right click on the VNC logo and select OPTIONS. Then go into connections and make sure the defualt port is 5900 and that you accept invites on that port.
Next, make sure you don't have a password set up, or you can set one up I just don't use one because no one knows my IP! After that, when you're at school, run VNC VIEWER. Then when it says enter IP, put in your homes IP address. Click on connect. You should connect. If you don't then you need to figure out why your IP from your school isn't being transfered to your IP at home. Either that or someone at home is on that computer or VNC itself closed.