Suggestions:
Pause the update for about 3-5 seconds, then resume. If this fails, then restart all of your internet related hardware (modem/routers, etc) then restart the PC. (Use RESTART not Shut Down)
And make sure you wait till its entirely downloaded before attempting to play, even if the play button is available.
If none of that helps, you may need to visit this thread and look for troubleshooting the battlenet launcher:
-Current list of known fixes and work arounds from the community and other sources!
Installing/downloading game files/updates
When it comes to downloading updates or installing the game, the speed is a known problematic issue. There are a couple of things you can try to resolve it:
You can setup a bandwidth limit using seven 9’s → 9999999
You can simply pause the download, then resume it after a second or three.
Also, do not use the Play button till your installation or download is complete even if it allows you to. This is known to cause problems.
Battlenet App hanging or not launching game etc,
Now in the case of problems with the battlenet app working correctly, IE hanging, stuck trying to download a file, not launching a game, some of these solutions may help:
Anytime you see it having login issues, make sure there isn’t a service outage first. A problem with the login server or a Blizzard server outage or a scheduled maintenance can cause login issues.
My first suggestion is restarting the App, or restarting the computer as directed above. Also checking the internet connection as well.
Next would be to log out of the app completely, then exiting the app. Next restarting the app and attempting to log back in. You can also log into the website via your browser to ensure your account can log in properly.
For instances where the app is stuck either trying to update a game or launch one, you can follow these steps from Blizzard: -Deleting Battle.net Files - Blizzard Support
If that fails to resolve the issue, then you would go with the directions here for uninstalling and reinstalling the app. -Uninstalling the Battle.net Desktop App - Blizzard Support