It was working until the update. I suspected Avast changed a framework/tech (flash, new library, etc.)
Avast - Privacy > SecureLine VPN
Your online privacy is not protected
Turn on your VPN to encrypt what you do online
X OFF
Have you checked a Country is selected to connect to?
Yes. Different ones too.
You can contact support: https://support.avast.com/en-us/contact/
But, keep in mind that they can take a few day to handle your situation.
Good luck! 
March, 4th : I got exact the same problem as you can read below:
SecureLine VPN will not turn on AFTER UPDATE and stays OFF instead - Windows 7
« on: October 21, 2017, 04:16:54 PM » It was working until the update.
Avast - Privacy > SecureLine VPN
Your online privacy is not protected
Turn on your VPN to encrypt what you do online
Right now I realize the far beneath earth Support: A given phone no, which is unvalid, the time one do not have to scroll through informations and the anger about paying for a product which will not work after each update and one can not handle or change by options e.g. the position and so on…
I’m on windows 10 with SecureLine and have no problems.
Have you tried doing a clean install ??? https://goo.gl/4Ptzkf