Errm... the only way to tell if the nosegear doors are correctly rigged on a Pa28R is to jack it and do a retraction as the nose bay doors are open with the gear down ie on the ground. Therefore, the chances of being able to spot anything amiss during a normal preflight would be slight unless you were looking specifically for signs of fatigue around the gear door actuator (rods) mountings (. One thing to watch for is that the rectraction rods have been fitted in the correct position in relation to the Y shaped retraction/drag brace. They are not murphy proof!
Hope this helps though as you have explained that the door departed company with the hinges, it would be equally likely that the doors may have been misrigged and not faired correctly. causing aerodynamic forces to impart loads into the retraction/drag brace to which they are attached. This brace also forms the overcentre downlock function for the nosegear.
HST