These are the errors I remember getting:
*Failed to open a required file
*Something went wrong while opening a file
*Whoops! Looks like something went wrong
All-in-one fix that SHOULD work(You may have to do all of these):
1. Make sure Internet Explorer isn't set to Work Offline
2. Update Adobe Flash (It sounds silly, but it actually works)
3. All of these, in order:
a) Delete the battle.net folder in %ProgramData% (Hidden files/folders must be enabled for this to be accessible)
b) Launch D3/SC2/WoW launcher; let it update, then close.
c) Launch Battle.net/Hearthstone installer
4. Should work!