OK, this was a weird one that I originally took the blame for. I'd noticed ages ago that for some reason my laptop's screen didn't go into power save as it should and I found out that it kept turning on everytime a song changed in YME. My desktop worked just fine. I thought that I'd caused it with the YME Taskbar Remote  and wasted a lot of time trying to "fix" the Now Playing window that I thought was causing it. I finally gave up since there is a very easy workaround: Just turn on your screensaver to go on before the power save turns off the monitor.

Someone in the IRC chat room asked about this last week (khit, you know who you are. I certainly don't.) and today I stumbled on something that I thought might finally "fix" it. So I added some code and wasted more time until I finally came to the conclusion that maybe, just maybe, the cause isn't the remote. Sure enough, just having YME playing will turn on the monitor owhen the song changes.

This lead to trying to guess what the underlying cause is so I tried the same test with Windows Media Player. Guess what? No power save at all, not even when WMP was minimized. 5 seconds later I remembered that there's a setting in the options window named "Allow screen saver during playback". Sure enough checking this enabled power save again. The thing is that checking this also fixes the song change power on in YME (since YME uses WMP for playback).

Long story short:

If you have the problem where your monitor won't go into power save mode when playing music, turn on your screen saver and set it to go on before power save.

Your second option is to go into Windows Media Player's options and turn on "Allow screen saver during playback", but I'm pretty sure this will also allow screen savers during DVD/video playback.