The thing Sixen mentioned can be accessed only if you're on Windows Vista or 7. You just right-click on the downloader and then click Run as administrator.
Try checking your internet security program first. If you have rules in its program list to let it through, go to Internet Explorer -> File, then make sure Work Offline isn't checked. Also check Internet Explorer -> Tools -> Internet Options -> Connection -> LAN Settings and make sure your proxy information is correct. If you don't use a proxy, make sure that everything is unchecked and hit OK. If that doesn't work, go back there and try toggling your Automatically detect settings box, then hit OK. Try the downloader again. If you made any changes, you may have to delete that downloader and get a new one from http://www.battle.net/account/
"I explode the healer with my awesome damage" - Ghostcrawler