I doubt anything “came loose” as everything is tightly secured in an iPad Pro. Everything you say points to a logic board issue.
What is more concerning is the potential history of this device and how (and by whom) was it “refurbished”. There’s a very real possibility that this device was always going to fail at some point either due to a poor repair or that something more fundamental was going on at the logic board level. For example, the screen may have been damaged, repaired and sold as refurbished. But a series of drops over time meant that the logic board was a ticking time bomb, ready to go off at the next, slight impact or drop.
As Peter suggests, you could open up the device and inspect it for anything obvious however keep in mind that the Pro series iPads are much trickier to work with the the Air/Air 2 and their clones (iPad 5/6) and you could easily cause a lot more damage just taking it apart. Take a look at the [guide|118536|guide] first.
If it is a logic board issue, board-level repair can be considered but these are difficult devices to work on as there is very little technical information available for them.