Ok so, just to clarify when you say "my desktop" you mean your mail server right?
On Nagios side:
Try to send an email using telnet from nagios through your mail server? (http://www.wikihow.com/Send-Email-Using-Telnet
You must at least have the right to connect to it!
Using the check_smtp
command, try to specify the port as well as the user name and password if your mail server is using authentication and see what it says:
check_smtp -H host [-p port] [-A authtype -U authuser -P authpass]
On your mail server side:
Make sure that nagios have the right to connect to your mail server via telnet your_mail_server port