Yep, that's a 17" cabinet alright. They have electronic fluorescent lamp ballasts for the the top and belly glass that can cause the problem you describe when they fail. Easiest way to test that is disconnect one, power it up and see if it quits power cycling on its own or not and then the other. If both them are good then I'd replace the power supply. The power supplies for that model are readily available and pretty cheap.
Just curious, what are the AC power cords in the bottom going to? They aren't normally there.