Do you have a second button, and is this computer a tower?
The reason I ask is because a tower is simple. The motherboard signal to reset is just a momentary on switch. You complete the circuit, power is delivered back to the motherboard header pin, and the computer knows to restart. Assuming this, get a secondary momentary on switch, and then wire them in series. A physical distance between the buttons is the easiest way to prevent accidental presses.
The ghetto mod version of this is taking to switch from another case, and slicing off the header connection on it. Take the current switch, and cut about half way between the header and switch on one of the wires. Take the switch you've cut the header off, and splice its wires into the switch you've cut half way. You'll have to press both buttons now in order to get a reset signal.
Alternatively, get a rotary key switch and wire it into series with the momentary push button switch. The computer cannot reboot if the key isn't rotated into place, and no amount of button pressing will allow it to happen. Of course, this means you'll have to keep the key somewhere nearby in case you actually need to reset the system.
If you're looking at a laptop, good luck. Modification there is a joke, so you should try going into software and changing button press requirement times. This also works on a desktop, but isn't an idiot resistant solution.
Edit:
To those who don't get how this works, let me explain.
The reset and power switches always have power running in them. The reason your computer doesn't power cycle is because there is no path to ground, because the switch is breaking the circuit (NO, or normally open switches are used). This means that a small piece of metal, like a screwdriver, could jumper the motherboard header pins and send the signal to boot-up.
The only reason polarity comes into play is for lighting. LEDs are utilized to indicate HDD activity and power. An LED is a light emitting diode, and diodes only pass power in one direction. Assuming that old school bulbs are used, the headers don't need to be marked for polarity at all.
