Here's the iFixIt guide to replace the power supply for this model Power supply. I would first make sure the AC in & DC out cables where not loose. Then I would check for any visibly damaged components.
If I didn't see anything I would do a little probing to check if the power button was working and check logic board was getting voltage. At this point you would need to have the system powered to check anything. Otherwise, I would just swap out the supply
CAUTION you can hurt your self as well as your system if you don't take proper steps. Ideally, you should have an isolation transformer to protect your self from the direct line voltage. In addition placing the probes directly on the power supply when you don't know what you are touching could damage it and the main logic board.