do you have an internal DNS server that is handling the domain for your active directory by any chance??
if so i suspect thats the problem, as i have a similar setup, mine looks like this:
my AD is myoffice.mydomain.com and my users can't get to *.mydomain.com as the DNS thinks that it is hosted internally somewhere.
The way to get around it - and there's probably a better way - is to add a Host Record aka an A record to the DNS entry for mydomain.com. Call it "WWW" and point it to the IP of www.mydomain.com, that way when a user requests www.mydomain.com it'll get routed out to the interwebs.
You can also setup mail (mx) records too, just incase thats not working either.