Welcome to the group! A video would help. Or at least some photos.
Are both the motors connected? If you remove them from the coupling do they move? Likely it is binding (too much friction, not level etc) or you need to adjust your voltage controller. I am going to say 80% confident you need to play with the voltage.
Chances are it's just the voltage. I do not know what electronics you have but if they are RAMPS 1.4 then you are looking for these
Also here is the wiki on the 1.4. Just turn the screw gently. One direction will give it more power. The other less. When it has too much power your motors will start making a thud noise.
EDIT post adding the video
Oh yeah that is binding. If you wouldn't mind putting the video on youtube to that the video can help people for years to come? Dropbox is a bit volitle.
I would also in addition to my advice in your other question take a bubble leveler to all the rods. It could be a distortion on your camera but it looks like the rod is a bit bent. Also in my Prusa (original) I used to have to make the motor mounts lose, as it did not fit all that well and had binding issues. Try making the screws loose enough so that they float and can move around a lot. The lead screws are less important to the overall stability.