Help with fixing LED night light that won't turn off
Correct me if I am wrong but it seems from the picture that the impact with the ground only created one fault: one O/C (open circuit) that you labelled: severed cable. 

The other components seem to be securely soldered onto the main PCB so I doubt the drop caused any other components to become faulty. 

It seems like the simplest solution may be the best here: strip, tin, re-solder (and maybe heatshrink) the broken wire to the correctly identified terminal of the PCB.