Firstly go to Appearance > Theme Option > General settings > Front Page On/Off and turn it off. Now, Go to Settings > Reading and select your static page from there.
You can still click on links to other pages, it is pretty much only hiding the main page. Please advise.
You can use WP SoonOnline Page wordpress plugin for this issue. Download it plugin from the link http://wordpress.org/extend/plugins/wp-soononline-page/screenshots/ and install it from the Plugins panel in your dashboard. The static page created by this plugin will visible by all not logged in wordpress users.