There is a setting on the Xbox under Settings, Console Settings, Remote.
This allows you to select Xbox 360 Media Remote or Xbox 360 Media Remote and Windows Media Center Remote.
If you select Xbox Remote only, your Windows remote should stop turning the Xbox on.
However, this won't help if you do want to use the Windows remote with the Xbox sometimes as it will mean the Xbox won't respond to the remote. I'm not sure if there is a setting that just changes the behaviour of the media button, the only thing I could think of instead would be to buy a universal remote and set the buttons how you want them.