Exchange 2013 will not send email

I have one server with 600 gig drive / 128 gig ram / windows 2012 standard for the domain controller and a second server with 600 gig drive / 128 gig ram / Windows 2012 Standard for exchange 2013.  Both servers are fully updated and show no errors in the event logs.

These are both in my shop trying to get working.  When I join the domain with a system and send an email it will say it is sent but I never receive it.  If I do the same in OWA the email stays in the draft folder.

I have created the send connector on the exchange box.  
Below is the error I am getting in the queue manager

 Identity: mail\5\103079215109
Subject: Undeliverable: Inbound proxy probe
Internet Message ID: <784e39fe-2ddc-4f17-a447-364467094133@mail.essgroup.local>
From Address: <>
Status: Ready
Size (KB): 9
Message Source Name: DSN
Source IP: 255.255.255.255
SCL: -1
Date Received: 9/22/2013 6:46:15 PM
Expiration Time: 9/24/2013 6:46:15 PM
Last Error: 400 4.4.7 Message delayed
Queue ID: mail\5
Recipients:  inboundproxy@inboundproxy.com;2;2;400 4.4.7 Message delayed;0;CN=Internet Send Connector,CN=Connections,CN=Exchange Routing Group (DWBGZMFD01QNBJR),CN=Routing Groups,CN=Exchange Administrative Group (FYDIBOHF23SPDLT),CN=Administrative Groups,CN=FirstOrganization,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=essgroup,DC=local


I am not sure what to do from here...  Please advise
TechnicalSolutionsAsked:
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TechnicalSolutionsAuthor Commented:
This was a lot of help.  The information that was sent to me was very helpful in resolving my problem.
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