You should try telnet to port 25 and don't login. If you're sending what could be an outgoing email, it is more likely to queue it.
MAIL FROM:<tedu@tedunangst.com>
250 2.1.0 OK g15si484689qej.92 - gsmtp
RCPT TO:<tedunangst1233141@gmail.com>
550-5.1.1 The email account that you tried to reach does not exist. Please try
550-5.1.1 double-checking the recipient's email address for typos or
550-5.1.1 unnecessary spaces. Learn more at
550 5.1.1 http://support.google.com/mail/bin/answer.py?answer=6596 g15si484689qej.92 - gsmtp