Looking around on Blizzard's forums you aren't alone.
The latest patch has screwed up the game for a huge percentage of players, I couldn't even get the game loaded up for 9 hours
The best you can do is close down any background programmes and downloads and wait for Blizzard to sort out the mess that this patch has made

This may sound stupid, but if you have any addons installed. Remove them, when i first started it up, i still had carbonite and all sorts still on. Disable them, and it should speed u. If this wasn't the problem, then i don't know, i'd suggest fishing in the forums for a solution.

Make sure addons are disabled and at the login screen turn your graphic settings all the way down untill you get in then reset them to match the way you like them.Reason for this is blizz messed with shadows and textures in this update

Might want to try and change your resolution along with the other options. That's what did it for me.

if got the problem 2 but fixed it tuttorial is at youtube