It's ok to take off the cabinet(the back of the monitor) and the metal shielding that covers the insides, just don't touch any of those insides like the capacitors or circuit boards, the capacitors can hold lethal voltages for years even when the monitor is unplugged. There are some capacitors and stuff on a circuit board near the power button so be careful when you're fixing it.
I have an HP P1230. It's mostly the same as the 2070sb(same insides, different cabinet and bezel). I'm not sure if the power button works the same on both monitors. Mine wouldn't turn on when I first got it(I got the monitor for free on craigslist). Here's how the power button was supposed to work on my monitor: the button itself(the thing you press with your finger) pushes a white piece of plastic, which in turn pushes the power switch itself. The white piece had fallen off, so it would just spring back without having the monitor turned on, and it also took less force to push the button in, so it felt 'dead' to me.
I had to take the cabinet off to get to the power button. I took off the bezel too, thinking I had to to get to the power switch, but that just caused me a lot of extra trouble, as I had to disassemble most of the monitor and put it back together just to get the bezel back on. The bezel on an HP P1230 is the front silver part, the cabinet is the part that covers the back of the monitor.