Hi,
there is a transistor on the top right corner marked as AH-16. Most likely it's defective.
Try to short the Collector-Emitter and see if the unit power on. If yes, change the transistor and you are good to go.
if i'm not mistaken here is the datasheet :https://www.onsemi.com/download/data-sheet/pdf/bcp53t1-d.pdf