A cabinet door that sags, won't close, or hangs crookedly is almost always a hinge screw issue. The fix takes five minutes.
Open the cabinet door and tighten every hinge screw — both the screws going into the door and the screws going into the cabinet frame. Most loose cabinet doors are fixed completely at this step.
If any screws just spin freely, the hole is stripped. Remove the screw completely. Dip two or three wooden toothpicks in wood glue and push them into the stripped hole. Break them off flush. Let dry for at least an hour, then drive the hinge screws back in.
Modern European cup hinges have adjustment screws that move the door up, down, left, and right. Turn them in small increments until the door sits correctly in the frame with even gaps on all sides.