vpn - Cisco AnyConnect Secure Mobility Client service can not start on Windows 7 64 bit system

I am using "Cisco AnyConnect Secure Mobility Client v3.1.04059" to establish a VPN connection to a campus network at a university.
When I start the VPN client (vpnui.exe) I receive the following error message:

VPN service not available.
The VPN agent service is not responding. Please restart this application after a minute.

However, when I try to start the required service - called "Cisco AnyConnect Secure Mobility Agent"- manually (using admin privileges) I get this error:

Windows could not start the Cisco AnyConnect Secure Mobility Agent service on Local Computer. Error 1067: The process terminated unexpectedly.

I get the same error when trying to start the service over an admin command prompt (net start "Cisco AnyConnect Secure Mobility Agent").

I have uninstalled and reinstalled the VPN client several times, which didn't help.

The problem first appeared when an auto-update to the latest version of Cisco AnyConnect was performed (which is not optional, but happens automatically every time the vpn client is started, so going back to the previous version does not work...).

How can solve this issue? What am I missing?

EDIT: I have uninstalled my avast antivirus software now and deactivated windows firewall. To my surprise the problem is still there, so it is not related to Avast antivir as I thought at the beginning.