It seems that the BlackBerry Messaging Agent cannot start. The Messaging Agent is the part that actually performs all the work of sending/receiving email, scanning the mailboxes, etc. Seeing as it can't start then nothing will work.
If you open the Windows Event Viewer and lookat the Application log you will see many events for the Dispatcher, Controller and Messaging Agent.
When you see a Messaging Agent with the 'afff4fb6'GAR-ISA01' agent 1: will not restart - reached the maximum of 10 restarts per 24 hours" event, there should be another from the Messaging Agent right before or after it with an error number in the description like 5302 or 5305.
Check there first. Don't rule out the DMZ being the issue, unless you've locked down what ports MAPI communicates thorugh then you need to open a lot of ports to ensure that you get proper communcation from BES to Exchange.
If you're concerned with security you can place the Router compnent of the BES in the DMZ and only 1 port is used to link the BES to the Router component and is completely safe.
Search RIM's TKC for it, BlackBerry Technical Solution Center
Let us know what you find.