Mitch, Brian is right that their is something fishy about your DNS record(s) for email. To my eye using the digwebinterface.com tool, it looks like you have an extra bogus MX record. dig is considered an authoritative tool--this is just the web based version of it.
For context, my club also uses GoDaddy for its custom domain: mindfulcommunicators.org
When I dig the mail.mindfulcommunicators.org records I get (w/ ANY option):
Code:
mail.mindfulcommunicators.org. 3599 IN A 50.19.253.65
When I dig the mail.businessandprofessionaltoastmasters.org records I get (w/ ANY option):
Code:
mail.businessandprofessionaltoastmasters.org. 2165 IN A 50.19.253.65
mail.businessandprofessionaltoastmasters.org. 2165 IN MX 1 mail.businessandprofessionaltoastmasters.org.
Note the extra record which is self-referential (circular). This is a key difference from my club's DNS which uses GoDaddy, is well established and whose email works fine. I am a bit puzzled how you managed to get this extra record.

You should talk to GoDaddy customer support about getting this extra bogus MX record removed.
To be complete, there is another MX record (dns is hierarchical) found by doing a dig on businessandprofessionaltoastmasters.org (w/ ANY option) which looks ok to me:
Code:
businessandprofessionaltoastmasters.org. 599 IN A 50.19.253.65
businessandprofessionaltoastmasters.org. 3599 IN NS ns57.domaincontrol.com.
businessandprofessionaltoastmasters.org. 3599 IN NS ns58.domaincontrol.com.
businessandprofessionaltoastmasters.org. 599 IN SOA ns57.domaincontrol.com. dns.jomax.net. 2017071000 28800 7200 604800 600
businessandprofessionaltoastmasters.org. 3599 IN MX 0 mail.businessandprofessionaltoastmasters.org.
The MX record should only exist for the top-level domain.
My club's top level domain DNS records (again... GoDaddy is our registrar)... pretty close:
Code:
mindfulcommunicators.org. 3599 IN A 50.19.253.65
mindfulcommunicators.org. 3599 IN NS ns43.domaincontrol.com.
mindfulcommunicators.org. 3599 IN NS ns44.domaincontrol.com.
mindfulcommunicators.org. 3599 IN SOA ns43.domaincontrol.com. dns.jomax.net. 2016081700 28800 7200 604800 3600
mindfulcommunicators.org. 3599 IN MX 0 mail.mindfulcommunicators.org.