Well your lens moves so that's a good sign. usually the gears go bad so that is not your issue.
From the look of your 2nd video I can't even see any red coming out of your lens. Maybe your camera wasn't picking it up? If indeed the lens isn't lighting up then the lens is most likely bad, the ribbon cables for it are ripped, or someone put the cables in backwards for the lens. I've seen that quite a bit.