To my knowledge there is not a lot of scope for wrong assembly as the "head" simply won't fit on if it is not correctly assembled and (I think) won't go together the wrong way. I am assuming it is a three bladed rotor type.
One test worth considering is to leave two of the three blades out and try operating the shaver with just the one. That can then be moved/rotated to each drive pin at a time. The older models had drive pins set into "resilient" (rubber-like) sleeves which in turn fit onto the primary drives. These can slip and fail to give enough torque to turn the blades if loose, oily or simply perished. If this becomes evident in a test then try pressing down on the visible drive pin(s) before testing again. My shavers are of this type (35+ years old) and I am less familiar with the later models - of which I have had a few but they didn't survive so well. My oldest one (still working fine, after a bit of surgery) was my first, bought in 1977, and that's not counting the antique two bladed one I used from first shaving but then parked after I got the "posh" one.