A dark Note II screen is definitely less fun than one that works properly. You did a good thing by pulling the battery out and you've given us some good information about the device's current functionality - the "buttons" at the bottom light up and it makes the sounds, but the screen doesn't come on. I think that we may need to try a master reset using the device's hardware buttons to see if we can bring it's screen back to life. Here's a link to the steps for performing a master reset using the hardware keys: http://support.t-mobile.com/docs/DOC-4866#Master_reset_using_hardware_keys_
Can you test this and let us know if it's working? We'll keep trying until it is
This happened to me but only after I dropped my Note II on concrete.. There is very little troubleshooting we can do in this instance, since we are unable to see the screen. If you have an SD card installed, remove the battery, and SD card. Restart the device without the SD card. If the phone comes back on as normal, there is something on the SD card corrupting the device, and the SD card needs to be formatted. If the screen is still blank, that lets us know the device is defective. If so, contact us, and we can review your replacement options.