So you set "Turn off monitor" to a sane value like 10 minutes and your lcd monitor goes blank but you can still see light coming from it, the backlight is still on. This defeats the purpose of the function as power is still going to the main power drainer, the backlight. I have this problem and I am using an XFX HD-577X-ZNFC with Catalyst drivers 10.1 on Windows 7 64 bit. I read on a forum that this is only an issue as of 10.1, if you use the previous driver (9.12) you will not have this problem. As of today, the 17th February 10.2 is released and I installed it and the problem no longer exists, the lcd goes off as it should.
Choose your version of Catalyst driver here: http://support.amd.com/us/gpudownload/Pages/index.aspx
Sleep and hibernate work as they should and the monitor goes off as expected. I use a Dell S2209w that goes into "Power Save Mode" when it is not being used by the PC and the lit power button on the bottom right goes from white to orange when not in use.