It is worth spending some time in highlighting some email problems and how to begin to solve them.
In general, there are only a handful of email problems and these are, in no order of importance:
SMTP server is not accepting connections
SMTP server is not accepting connections from your network
POP server is not accepting connections
You can not log on to the POP server,
Your IMAP server is not accepting connections,
You can not log in to the IMAP server.
Problems 1, 3 and 5 are relatively simple to check. One method is using a port scanner, while another is just to telnet to the port and check whether you get a reply.
In the case of POP3 and IMAP, you may not get a reply before you have actually attempted to log in.
With SMTP however, you should get a reply from the server as soon as you connect.