i cant make out anything in those pics far too blurry sorry they are no help
also your 1st video is no use in it you are only looking at it when it is off turning it around shows me nothing.
the 2nd video proves my point, the drive only powers the laser to see if a disc is there, and the worm gear only nudges it a bit not enough to force the gear to buzz, i bet it buzzes like mad when its in the 360 as the 360 will make the laser jump to the edge of the disc during booting.
in the 3rd pic notice the large white plastic part that is attached to the laser.
inside it is a spring that forces a small plastic part against the worm gear check that it is there i have taken a pic of a liteon i have for your reference.
you look at this from the top of the drive not the underside
If this spring is missing then the worm gear cannot push the laser back and forth and you get an awful biuzzing noise.
I first encountered this sort of issue back in the PS2 days the lasers in those used a plastic lever arm on the gear instead of a spring; that over time with heat and stress developed creep and failed.
my m8 sent me over a drive ms25 from england a few years back and i modded it for him .
unknown to me, the spring popped out during transit and when he got it back he phoned me with the same problem, buzzing and no loading.
there are only two moving parts in the drive that can make a buzzing/grinding noise - the tray mechanism and the worm gear. if the spring is there, look over the tray mechanism
i have also added a pic of a functioning tray mechanism
you have to take the tray out to see this fully.
open the tray and flip the drive over and you will see two little tabs you have to push to slide the tray fully out.
compare your drive to my pic to make sure the gears and belt are all in place ok.
if all else fails buy a new drive and flash it with your key.