you can have a look at the ADL SDK: http://developer.amd.com/tools-and-sdks/graphics-development/display-library-adl-sdk/
ADL gives you the possibility to get some state information on the connection status, e.g. if a monitor is connected via DisplayPort, DVI or using a dongle. You can have a look at the functions: ADL_Adapter_ConnectionState_Get and ADL_Adapter_ConnectionData_Get.
As far as I know you cannot check a monitor state like "power on" or "power off" since as soon as the monitor is powered off the connection is no longer present. If you know that a monitor is connected to a specific port you could check the connection status and if it shows up as not connected it implies that the monitor must be powered off.