I have a monitor that is the best one I have: widescreen, says "HDMonitor", and flat LCD. I really like to use it. But the problem is, it randomly turns off! I mean, the screen ceases to show anything, but the power light stays on. To temporarily fix it, I need to turn it off and leave it off for about 5 minutes. This can be a big problem, especially when playing Minecraft. So, does anyone know offhand how to fix such a thing (for cheap or free)?

My initial guess is that some component of the backlight is on the way out - when it stops showing anything, is the screen completely dark or does it glow slightly? (Try in a room with the lights out).

Has it been making any funny noises? (Chirps, squeaks, whistling etc?)

If the display uses a CCFL backlight you may just need to replace the inverter.

No, completely dark, and no noises.

If you can (carefully!) dismantle the display you could check to see what the condition of the inverter is - it's usually a long thin PCB with some coils on it (like this example). Be careful as CCFLs run at a high voltage, so only do this with the monitor disconnected from the mains. You can check to see if the capacitors have leaked or are bulging, as they are a common point of failure.

Alright. I probably can do it. Our laptop had a similar problem (only I could see that only the backlight was going out), and it no longer has it. Why I don't know; I took it all to pieces and put it back together again without doing anything too meaningful otherwise.

Shine a flashlight at areas of the display where you know you there should be something that would be easily visible. Sometimes helps to hold the flashlight at an angle to the display.

If you can see something, it's the backlight/inverter system. If not, it's probably something else.

I haven't tested it 100% (it is too intermitent by far), but I am quite sure the screen entirely looked off, besides the power button being on. :/

Most color LCDs do look completely off if the backlight isn't working, even if they are displaying something.