Your Notification has a PendingIntent. This is used to define behaviour for clicking the notification. A pending intent has an intent as well, this intent contains info about application to launch, or in general, what to do after clicking the notification.
In your example, however, the intent that is included in your Pending Intent is:
// Empty intent, not doing anything
Intent intent = new Intent();
E.g. your intent does not define what to do. Change your intent to something like this:
// New Intent with ACTION_VIEW:
Intent intent = new Intent(Intent.ACTION_VIEW);
// Activity to launch
intent.setClassName("your.package.name", "ActivityToLaunch");
// Intent Flags
intent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);