There are many reasons your email might not be working. Almost all of them have to do with your computer, software or internet connection (ISP).
To test the web server, try logging into http://yourdomain.com/webmail. If webmail is working, the server is working properly and the issue is elsewhere . . . at least in 99.9% of the cases.
Make certain you are connected to the internet by going to a web site you have never visited before.