In the former case you can simply replace the nameserver(s) with one known to be working, as above (but do the same ping test on that one). In the latter case, you need to look at why you don't have Internet connectivity; your VPN setup instructions will hopefully provide some help here.

Is My VPN Working? - Cogipas.com Mar 21, 2020 How to Check your VPN is Secure & Working in 2020 - VPNFTW Jan 03, 2020 Is my VPN Working? Here's How to Check if VPN is Leaking Dec 20, 2019

Oct 03, 2019

HOW TO CHECK IF YOUR VPN IS WORKING OR LEAKING! - YouTube

How to Find Out if your VPN is Working as it Should

VPN is a great for boosting online security, defeating Internet censorship and bypassing geo-blocking. It’s not difficult to set up a VPN connection on a PC, a mobile phone or a tablet. However, for VPN users, there’s a very basic question: How do I know if my VPN is working? How to Check and see if your VPN Connection is Secure