This is an old one, but will save me looking it up.
Use the following to do a simple test email to a SMTP server (assuming connectivity/DNS) is ok.
telnet SMTP.SERVER.COM 25
helo SERVER.COM
mail from: user@server.com
rcpt to: user@destination.com
data
type the body of your email
.
quit
The email will be sent or an error produced that can be used to diagnose any problems.