Shoutbox

Apart from a PC you can also email and sign in to Messenger from a mobile phone / PDA / Xbox / Laptop / Mac / Someone else's PC.

In all cases you will need some type of internet connection, but you can get that in various way apart from just your ISP at home (mobile phone provider / Public access points / Work / School / Friends / etc. / etc.).

Just talk to the person when you see him/her online. If they don't reply they just don't want to talk to you and you should probably just get over that.