The motor and daughter circuit board should pull right out. Find the set screw holding the lid mechanism linkage to the motor (second photo). If your motor wasn't opening the lid or making a clicking sound, this has probably come loose.

The shaft of the motor is a D shape, and the set screw needs to be tightened on the flat side - the line in the third photo. is parallel to the desired flat side, and the arrow shows the direction the set screw should be.

At this point, you may need to power the motor and allow the motor to rotate so the flat side can be lined up with the set screw. On the main unit, screw the battery housing back on (undo the step at 1:11 on Surepet's video), insert batteries, and connect the ribbon cable, paying attention to the direction of the connector clip.

Press the open/close button on the daughter circuit board so the motor attempts to move the lid. Then pull one of the batteries out when the shaft is aligned as seen in the third image.

Be very careful not to touch any circuit boards with metal tools or dirty hands, or to cross any wires when you do this (it's ok to interact with the smaller circuit board to press the open/close button). Once you've gotten the shaft aligned, the set screw tightened, and tested that the motor works as intended, take the batteries out.