The most likely problem is the battery, usually the battery failure, and for low-cost charging desk lamps, there may be a problem is the internal connection cable loose after a fall.
If you have some basic electrical and electronic circuit knowledge, you can try to disassemble the charging lamp and visually check the internal connection cable, especially whether the battery connection cable is connected reliably; If all is normal, you can try to use a multimeter DC voltage file to test the voltage at both ends of the battery and whether the voltage changes when connecting the AC charger.
If the voltage rises after the connection, it can be basically judged that the battery has failed; If there is no change, it may be some damage to the charging connection joint, poor contact and other reasons, and then for this part of the circuit with a multimeter resistance file or diode file measurement, it should be easy to find the problem.