How long has your DNS name been registered for this MX record? These can take about 48 hours to propegate.
A good test would be to use your mail client to go directly to the SMTP mail server (by IP address or name – each is a good test), over the Internet, and deliver the mail directly to it. If you cannot do that, then there is an issue with either DNS (if the name fails) or the firewall/SMTP server (if IP fails).
I hope that helps!
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