I've got the solution for this but wanted to share the problem and answer.
When my Polycade Lux first arrived I plugged it in and pressed the power button on the bottom of the machine and nothing happened. Here was my solution.
I opened the case and looked at the chord for the power button and saw that it was not plugged into the motherboard. Here's a pic of the button from inside the case.
I looked up the manual for the motherboard and found where the power button is supposed to be plugged. If you look on the left hand side of the motherboard there are lots of pins. See the pic below for the location.
In the close up pic you can see there is a white area that has 9 pins (5 on the left and 4 on the right). The power plug needs to go into the lower right two pins. Red cable on top and black cable on bottom.
Hope this helps anyone else in the same situation.