This points to all the classic signs of the Send As issue. If you look in the Application Log you should see an event from the BlackBerry Messaging Agent referencing your account. There should a 80047005 type number in it. Depending on what that number will tell us if it's a permissions issue or a DC/GC issue.
If the error you see is:
MAPIMailbox::Send(ppMAPIMessage) - SubmitMessage (0x80070005) failed
Then it's a permissions issue. You could either, a) be somehow linked to one of the protected groups, or b) Your account just doesn't have the Send As permission.
A test you can try is the one posted earlier by juwaack68. Log in to a PC as your BESAdmin account and open Outlook. Create a MAPI profile for your account and try sending an email. If this fails it will tell you that you don't have rights.
What this does it mimics how the BES sends email. If the BESAdmin cannot send on your behalf then you won't be able to send anything. Period.
I worked at RIM and dealt with this issue more times then I care to count. Believe when I tell you that what everyone here is telling you is valid. This is a crappy issue brought on Microsoft, not RIM, and can be a b*tch to fix sometimes. Sometimes you can just add the permission and wait for the mailbox cache to clear and you will work fine. Other times people have to use DSACLS to forcefully write the permission to the mailbox.
Follow this KB as posted earlier by penguin3107:
BlackBerry Search Results
It has everything you need to find the permission, place it on your mailbox and it even links to good MS articles as well.
Follow it and ask any questions if necessary. Let us know how it goes.