As @arpydays mentioned, do you have an HTTP proxy configured for your browser? That would explain why HTTP requests from a browser are working, but other traffic (like ping) is not. Have you added a default route to the BIG-IP (under Network >> Routes)? Are you using SNAT? The easiest thing to try is Automap SNAT. It is further down in the VS configuration, under "Source Address Translation". SNAT may or may not be required depending on your architecture. Also, ensure that "Address Translation" and "Port Translation" are not selected (ordinarily, setting the Type to "Forwarding (IP)" should unset those, but it's good to check).
Nimbostratus
