The button on my montitor recently stopped working so it cannot turn it on an off. I will need to get a new monitor eventually, but for now, is there a program that can automatically turn the monitor on and off with the keyboard or mouse?

you could put it into standby through normal windows but if you want to switch it off completely then you'll have to unplug the mains lead from the back! Simon If at first you don't succeed, hide all knowledge you even tried.

To open Power Options, click Start, point to Settings, click Control Panel, and then double-click Power Options. If Turn off monitor is not available, your monitor does not support this feature. Using Power Options in Control Panel, you can adjust any power management option that your computer's unique hardware configuration supports. Because these options may vary widely from computer to computer, the options described may differ from what you see. Power Options automatically detects what is available on your computer and shows you only the options that you can control. i_XpUser

You might want to venture down to a repair shop that builds systems. Ones that do networks is a good place to find good deals on used equipment. I bought a 17 inch Sony Trinitron for (you sitting down?) 20 bucks. And it has a killer picture. That sounds like the relay that locks on when you hit the switch has gone bad. At current bench rates it's just not worth getting it fixed.