Black unresponsive screen on iPhone 6s. HELP!

I am not much of an expert in this field, but from what I can see in your post, it would either be a faulty connection between the screen and the phone, or a broken backlight. If it is a faulty connection, follow the iFixit steps to for a screen replacement to find how to remove the screen connectors, and then re-attach them. If this doesn't fix the problem, it could be a broken backlight. You mentioned the screen appearing dark blue, and this could be a symptom of a broken backlight. Try shining a torch onto the screen while powering the phone on. If you can see the icons on the screen from the light of the torch, then it is most likely a backlight issue. That repair is out of my league, so I would suggest posting another thread centred around replacing your backlight, and see if you get a response from a more competent person than myself.

Hope this helps!