Why Doesn’t the Screen Turn Off When Playing Music on Windows XP?

Try MonitorES. You can find more information about this little app on Lifehacker:

Tiny, portable utility MonitorES not only turns off the monitor when you lock your PC, it also pauses almost any media player and even sets your Google and Yahoo IM status to away. We've written about this utility before, but since then it has updated with support for nearly any media player, added support for Yahoo Messenger, and you can now use it to simply pause your media with the Pause key. As before, you simply need to launch the utility, set the options, and the next time you lock your workstation your monitor will turn off, and your media will pause.

This looks like either a driver issue or a DirectX issue. I'd recommend completely uninstalling the sound drivers, then updating them with the newest version available for your hardware, and grabbing a copy of the latest dxredist from Microsoft and installing that as well.

Just because you can play sound through Flash doesn't mean there isn't an issue with the sound driver, as Flash doesn't leverage DirectSound. Make sure to uninstall/reinstall and not just update in place, as that also makes a difference, especially in issue where the old driver is corrupted.