Have you checked if the motor gets any voltage?
If it does, then either the motor itself is dead or the belt are worn out...Both scenarios are unlikely in my opinion.
When you take the tape deck apart, you have two layers of electronic boards. One of them is the micro switch board with a lot of microswitches on it. This one needs to be checked. It seems very strange to me that it is doing nothing at all right now but I am sure it is fixable. Has it worked beofre or did you get it like this?
I think I can hear the motor running in your video.
Not sure though.
Try this if you are afraid of opening it: when nothing is pressed on the keys, spin the capstan manually counterclockwise.
Maybe the mechanism is just jammed for some reason. Doing this should free it up if that is the case. If it spins freely when you turn it, loose or gone belts are most likely the issue. If it is hard to turn that means the best and therefor the motor are giving some resistance...so they are present at least.
It's hard to diagnose the issue from the video though...you may have to open it up to fully resolve the problem.