When you open a computer case, there is a circuit board with the on off button plus reset (on some) you unscrew it, mount it behind a standard push button (at the back of mine- generally fairly long reach) without a microswitch, so every time you press it it pushes back and hits the on off button.
With the monitor if you took it out of its casing for mounting like I have, you find that if you leave it on it stays on. So when you turn your computer on the whole thing comes on.
Really wouldn't recommend you try to do it from the mains only. Because if you have problems your playing with hot hardware. I.E its on! If you use a button its off. Although you could do the same with the monitor button.
This techinque works well. Most computers (if not all) use a separate circuit board - small thin easily mountable. Take care to check how its mounted as you unscrew it and mount it in a similar manner.