1) This is almost certainly NOT a DH issue
2) When you say no messaging of any kind has worked, what exactly do you mean? Moodle 1.9.x comes with built in chat and messaging. Moodle messaging uses a pop-up and will fall back to e-mail if you set it to. Are you saying that messaging between two persons logged in to Moodle does not work?
3) If you have not blocked it, Moodle messages will be dished off to the same e-mail process the Moodle uses for all other e-mail, so if you get any e-mail from Moodle, it is almost certain that you are not getting messages e-mailed when the recipient is off-line because that feature is blocked.
4) I did check the forums but found nothing from you posted. I would beware reading forum posts instead of documentation as they can easily mislead you.
I can likely fix things for you for a price or you can post to Moodle.org with specific details, including specific details of exactly what you have done or have not done and exactly what is or is not working. As I mentioned, as long there is mail coming out of Moodle to a user, then it is highly unlikely that the failure of that user to receive an e-mailed Moodle message has anything to do with DH.