Electronics riddle: After dropping on the floor, LED flashlight only works with a 3V supply instead of its normal rated 1.5V
If the flashligt worked on a 1.5 V D-cell it has to have a DCDC boost converter otherwise it cannot make a LED light up as most LEDs need at least 3 V for that.

The drop could have caused a fault in the DCDC converter. Depending on what and how a component breaks in such a DCDC converter, the input voltage might still reach the output. 
In that case, applying 3 V at the input might indeed light up the LED.

The circuit you see might be simple as it is just a switch. My guess is that there is a more complex circuit close to the LED.