Every monitor I've owned since the early 2000s will switch itself off (or at least go into a standby state where the screen is entirely off and there's a tiny blinky LED indicating that it's still powered) after a period of inactivity. I know some monitors never give up waiting for a signal but at this point maybe it'd be simpler to treat yourself to a new monitor?

Edit: Oh, you're talking about things waking your computer up? Maybe turn off 'wake on USB'? Although that's less convenient otherwise. I know when my desktop computer is fully hibernated, mouse motions don't wake it but button presses do. And you can get into this state (assuming Windows 8+) by right clicking on the Windows icon / 'start' button and selecting 'sleep'.