This doesn't appear to be a Diablo III crash but a Battle.net Desktop app crash. I'd recommend a few things here:
Step 1) First Delete the Battle.net Desktop app cache following the steps Here. Don't run the program after doing this.
Step 2) Uninstall the Battle.net Desktop app and reinstall it to your Operating System C:\ drive. This will help avoid any major permission issues.
Step 3) Before running the battle.net Desktop app again make sure of the following: - Secondary Logon is enabled. - Drivers are updated for the Operating System and video drivers, help with this can be found Here. - Disable any background programs that have Overlays.
Retest! If the issue continues try running the Battle.net Desktop app again while the system is in selective startup.