New Twiddle

application.controller.js

import Ember from 'ember';

export default Ember.Controller.extend({
  theService: Ember.inject.service('theservice'),
  actions: {
  	buttonClicked() {
    	this.get('theService').emitButtonClicked();
    }
  }
});

application.template.hbs

<br>
<br>
<button {{action 'buttonClicked'}}>Global Button</button>
<br>
<br>

{{outlet}}

{{link-to 'Go to first route' 'first-route'}}
<br/>
{{link-to 'Go to second route' 'second-route'}}

first-route.route.js

import Ember from 'ember';

export default Ember.Route.extend({
});

first-route.template.hbs

First component:
{{my-component}}

Second component:
{{my-component}}

my-component.component.js

import Ember from 'ember';

export default Ember.Component.extend({
  theService: Ember.inject.service('theservice'),
  
  doSomethingWithInput() {
  	this.set('randomProperty', true);
      console.log('Do something with input value: ' + this.get('inputVal'));
  },
  
  subscribeToService: Ember.on('init', function() {
    this.get('theService').on('buttonClicked', this,  this.doSomethingWithInput);
  }),
  
  unsubscribeToService: Ember.on('willDestroyElement', function () {
    this.get('theService').off('buttonClicked', this, this.doSomethingWithInput);
  })
  
});

my-component.template.hbs

{{input type='text' value=inputVal}}

router.js

import Ember from 'ember';
import config from './config/environment';

var Router = Ember.Router.extend({
  location: config.locationType
});

Router.map(function() {
  this.route('first-route');
  this.route('second-route');
});

export default Router;

second-route.route.js

import Ember from 'ember';

export default Ember.Route.extend({
});

second-route.template.hbs

First component:
{{my-component}}

Second component:
{{my-component}}

services.theservice.js

import Ember from 'ember';

export default Ember.Service.extend(Ember.Evented, {  
    emitButtonClicked() {
      console.log('EmitButtonClicked');
    	this.trigger('buttonClicked');
    }
});

twiddle.json

{
  "version": "0.4.10",
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.9/ember.debug.js",
    "ember-data": "https://cdnjs.cloudflare.com/ajax/libs/ember-data.js/1.13.11/ember-data.js",
    "ember-template-compiler": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.9/ember-template-compiler.js"
  }
}