Unfortunately you cannot just swap drives unless the laptops are exactly the same model as the drivers for various internal components will be different and problems will occur. If you just need to get files off your son's HDD then you will need a 2.5 Sata caddy. Something like these. Ebay.
I would imagine that dropping the laptop has jarred an internal connection loose which may or may not be repairable but likely to cost more than the PC is worth.