The simplest answer is to make a request to the web service! Anything else you do will tell you if you can talk to some particular host or other, but that's not really what you care about... you care about whether or not you can talk to that particular web service. The web service being down is equivalent to the internet being down, as far as your app is concerned.
Find a cheap and harmless request you can make as a test call, and use that. Of course, just because you have a connection now doesn't mean you'll have one in a couple of minutes... so you should still make sure that your app doesn't actually crash when the connection goes away. That should actually be your first priority IMO: making it fail gracefully.