Not to deter from my previous post which is so much more important but I've had a number of questions from people who were not able to log into Dalaran and I figured I'd throw those a bone who didn't figure out what the problem is yet.
I've heard of people suggesting re-installations or checking their internet connection speeds etc. and while that may contribute to solving the problem the true culprit usually is:
The Questhelper addon adds a tremendous amount of load on login as it tries to calculate the various quest stati and pathing information. In fact, as good as the addon may be it's often the source for various random disconnects/login problems.
If you are experiencing problems logging into dalaran or you have a character stuck there that you can't access turn off questhelper and if that doesn't help turn off all your addons before trying to log in.
Then relocate to a quieter place (pretty much any place that isn't dalaran really) and turn your addons back on.
Incidentally you should try to update the addons you use to the latest versions since a lot of them can generate errors that aren't visible per-se but can seriously slow your gaming experience.
For shits and giggles turn off all your addons and compare it to running with addons, if the difference is significant then you should consider a) updating your addons or b) replacing addons that cause problems.
Just a quick heads up for those fighting the DaLAGan monster.