A friends lamp broke so this is a reinforced replacement. Will require finish drilling the premarked holes. I used M3 12mm counter sunk screws for the outer holes. If the nuts dont fully counter sink into the plastic then use a soldering iron to heat the nut just enough to soften the plastic then tighten the screw to pull the nut into the plastic. The same can be done with the inner screw head if the edges are up too high. All the other holes are 1mm. These may need to be enlarged to around 1.5mm to 2mm.

It may be possible to replace the hinge without removing the bottom plate. If the white wire to the LED's is long enough then you will be able to gently pull the tube off the hinge without stretching the wire. Then you can simply just replace the hinge.

Otherwise:

Gently and slowly remove the rubber pad from the bottom trying to not leave the glue on the base plate. Remove the 5 screws and set the bottom plate aside. Unplug the battery (hold the white plug on the circuit board while pulling and wiggling the connector apart.

Unscrew the circuit board from base. Unsolder the red copper and plain copper colored wire from the circuit board. Make a note of which wire goes where. Remove two screws from oval post. Slide apart being careful with wire.

Now you can disassemble the hinge. Some minor filing may be necessary on the egdes of the post insert. You will need tweezers to fish the wire back throught the hole in the base.

Resolder the led wires to the circuit board. Leds are polarity sensitive. Connect battery and test leds. Then and reassemble base.