Enqueing External JS on the remote server JS

You use $ in custom.js file and probably that’s the reason, because jQuery is included in WordPress in noConflict mode.

You can replace $ with jQuery in custom.js or wrap the code as shown below:

(function( $ ) {

    // --- your code ---
    $(document).ready(function() {
       //...
    });

})(jQuery);

Or

jQuery(document).ready(function($) {

    // code from file whithout line "$(document).ready(function(){"
    //...

});

More about using jQuery in WordPress you can read in “JavaScript Best Practices” on codex.