He loves pushing buttons. In particular, he's attached to the one that turns off my PC. How do I stop that action from turning off my computer? I really do not need that archaic button, anyway.

open up the case and unscrew the on button. or get a spray bottle and spray him whenever he presses a button

How old is he? This is key.

Simplest fix would be to tape cardboard over the button.

Do you use that button to turn it on?

I second the cardboard advice, we also used it to block up usb ports to stop little ones poking stuff in.

I do not turn my computer off ever, but I suppose in extreme cases I'd need to turn it back on after a power outage or something.

Well, I asked because most of the suggestions would have made it impossible/inconvenient if you turn it on that way. I was guessing you wanted a software solution maybe?

Anyway, the cardboard seems reasonable. If you rarely need it it won't be an issue. You could build a flap and velcro it shut, but maybe that would be even more tempting

Buy a new PC power-switch (Google it, there's plenty of retailers) and wire-it INSIDE of the case. I'd do the same for the reset button as well. Heck, you could be super-tricky and drill a small hole in the case and make the power-switch accessible via a straightened paper-clip.

That, or just put the case someplace where the kids can't reach. It's the low-tech way to keep dogs/kids/gnomes/short people from touching your stuff.

Tape and cardboard, yo. Worked with my daughter.

Go to Control Panel -> Power Options -> Advanced

There's a drop down that says "When I press the power button on my computer", change that to "Do Nothing". You'll still be able to turn it on with the button, just not off.

This solution needed 3 month. Not really nerdy :-)

Other solution:
Don't play with your computer. Play with your son ;-)