Varnish 4.0 vcl for Drupal 7
The VCL you have linked to and your example in the question show you only using one backend. In this case using the probe to do a health check serves no purpose. As per drifteaur's answer disabling probe resolves many 503 issues and as you have no need for it, problem is solved.

However, if you are testing working towards rolling out on multiple backends then it still needs to be fixed(understood).

Looking at the VCL you linked (https://github.com/mattiasgeniar/varnish-4.0-configuration-templates/blob/master/default.vcl) it uses many sections which have been taken from https://www.varnish-software.com/ so we can presume (hopefully) that they are correct.

Currently, your probe is checking the response from "/ping" at your host and port, 127.0.0.1:8080, so that is 127.0.0.1:8080/ping .

If your set-up is multiple virtualhosts on one server with varnish sitting infront then using probe like this will not get a response(as this full url has most probably not been configured) and in turn this will lead to the backend being marked as "sick / unhealthy" and a 503 will be produced as Varnish will not even attempt to access the backend.

To confirm that it is your server setup add the following to your probe

backend default {
    .host = "127.0.0.1";
    .port = "8080";
    .probe = {
              .request =
              "HEAD / HTTP/1.1"
              "Host: www.EXAMPLE.com"
              "Connection: close";
              }
}


You will need to change www.EXAMPLE.com to a real domain you are using on the server.

If this gives you 200s rather than 503s than it is safe to confirm that using probe as you were with your server set-up was incompatible.

Probes info: https://www.varnish-cache.org/docs/trunk/reference/vcl.html#reference-vcl-probes