Can you please try the following steps? There's quite a few but since this issue can be caused due to a few different reasons, we need to make sure we go through everything.
1). It's mentioned above, but we really do need to make sure that you remove the Battle.net Tools folder. This should force the update agent to well, update, and the new version should hopefully work when updating:battle.net/support/article/deleting-the-battlenet-tools-folder-windows
2). Make sure you delete the Updates
folder in your game directory, this should just be in the base directory of whichever game you're trying to patch.
3). Check your Internet Explorer settings. The Launcher uses Internet Explorer no matter which browser you have set as your default. Go into Internet Explorer
> Internet Options
> LAN settings
and make sure that you de-select Automatically Detect settings
And make sure that you haveUse Automatic configuration Script
and Use a Proxy server not checked.
4). Remove any .mfil
files from the game directory, then launch it again. This will force a repair of the client, and ensure there isn't an issue with the client itself.
5). In case the issue is related to another program interfering, try running the game when Windows is in a Selective Startup
mode. Just to ensure nothing else non essential is running:battle.net/support/article/shutting-down-background-applications
6). Make sure that Secondary Logon
service is enabled:battle.net/support/article/enabling-windows-secondary-logon-service
Let us know if you still experience issues with checking for updates after this.