I updated Nvidia Driver from 306.97 to 337.88. Aero stopped working right after the installation was finished.
I have tried using Troubleshooting, re-running Windows Experience Index assessment, restarting DWM service, rolling back the driver, trying previous stable driver version 335.23 and installing 306.97 anew.
After each of these actions the Troubleshooter either does not detect a problem or says DWM is not running as well as color depth is too low. However, the depth is set to 32-bit and DWM service is running.
This is the result of Troubleshooter:
How do I get Windows Aero back up and running?