Glass broken. If glass or plastic is flat and rectangular, you can easily remove it (usually by taking out the bolts in the base of the case) and replace it with a new glass cut to size. But if glass is curved, round, oval, etc., return clock to maker for repairs.
Plastic case broken. Clean cracked edges and coat with plastic-mending adhesive. Clamp edges together for 24 hours.
Electric clock doesn't run. Examine cord for a break. Because clocks are rarely moved, their cords seem to get stiff with age; and then the insulation on them sometimes breaks when the clock's position is changed.