Surface dock won't work - how do I start to diagnose?

Hi all! Lately my Surface dock (the newer brick type) won’t work at all, and the area around the power plug gets really hot. I managed to open it up, and sure enough, the power brick connector and surrounding components (resistors & capacitors) are getting really hot when plugged in. I’m hoping that this is just a problem with the power circuitry, and the rest of the board is OK.

My question is, how do I get started with diagnosis and find the fault? Do I look for short circuits, or faulty components? Appreciate any help in advance!!