"Secure Connection Failed" only when using VPN

Check the details on the certificate that the browser is stating is bad. If the certificate comes from your company's domain, you are receiving an SSL certificate from the VPN concentrator and then making the connection on your behalf via a web proxy. This is typically done in order to do Deep Packet Inspection of SSL based traffic. If you make the connection to the proxy and then they make the connection to the https site for you, the proxy can decrypt the transmission because they have control of the necessary keys to view into the traffic which would otherwise be encrypted if you made a direct connection to the server from your browser.