You do not need to download chess.net for windows (the client software) to be able to play on chess.net. You can also try connecting to the server using chess.net for java, which requires no download. To try this, go to
http://www.chess.net/java.htm This only requires a working java plugin, which is standard in most popular browsers.
If you are using linux on the school servers, you can also try xboard, which is standard on most common linux distributions (so no download required).
If you still can't access the site, your school is probably blocking the ports required. In the java client, try changing the port from 5000 to 23, maybe that one is not blocked.
Let us know how it goes
