Is there an easy way to fix a plastic Electrical box, short of replacing it?

If there is enough of a lip on other parts of the box, you can drill a hole and screw the mounting brackett into those new holes. Most mounting brackets will turn so you can align the holes needed to mount the light.

Or just remove it. Since it is plastic, take a hammer and screwdriver (or cold chisel) to break it up and pull it out.

At a guess the sensor has bit the dust. If you don't know anything about electricity I wouldn't go opening everything up. What jim said was the best. A volt stick looks kinda like a pen and will glow red and make a buzzing noise when its near something live. Because the house is from 1941 you might get false readings however. Alot of old places are wired "loop at the light". That means at all times there will be a live wire at the light, its just not plugged into the light. Even with the switch turned off there can still be a live at the light. So be careful.

If the box is vertical mount the bracket for the light horizontal across the box with plastic anchors.

As long as the wires are still tapped inside the box you have no electrical code violation and it is safe.

And if the bod is horizontal mount the bracket vertical.

There is no rule that the bracket has to be mounted on the box.

DRILL HOLES ON EITHER END OF THE BOX

AND TAKE A PC OF 1/4 IN. PLEXIGLASS MAKE A COVER FOR IT AND THEN DRILL A HOLE IN THE MIDDLE OF THE PLEXIGLASS TO RUN THE WIRES OUT,USE THIS AS YOUR BASE TO PUT YOUR NEW FIXTURE ON. TRY IT--IT WORKS.