The first thing to do is always to test the resistance across the power supply to make sure there are no shorts. To do this, put the meter in resistance mode, connect the positive test lead to the positive power in, and the negative test lead to 0V (repeat across all combinations of pins on a multi-rail powered device, which I guess the norns shield is not). The resistance should start out very low but quickly rise to at least tens of thousands of ohms if not more as the decoupling capacitors charge up. If it stays at or close to 0 ohms, you have a short somewhere, which needs to be dealt with before you power up!
With access to the schematic you can do further testing without power, but typically if there are no power shorts it’s fine to plug in and see if the thing works. Test all buttons, LEDs and whatever, if some don’t work, check their connections, their multiplexing chip, etc.