Why can't I access iChat on my own laptop in a public library? Or Vuze.

Because the public library has to be very careful about what they allow to go through their wires. You could be a right-wing Muslim PETA terrorist looking at pictures of 12 year old girls for all they know.

They block ports. Most likely everything besides port 80 (HTTP) is blocked. iChat uses 5190 and I’m not really sure why I know that without looking it up.

Basically they don’t want you gaming and slowing down the connection for everyone. Would you be pissed if some wanker was torrenting porn causing your page loads to slow to a crawl?

Agreed. Prob trying to control streaming and data hungry traffic.