To check that a monitor is powered on in Windows 10, here is the command-line:
C:\Users\Vikram>wmic path win32_desktopmonitor
Availability Bandwidth Caption ConfigManagerErrorCode ConfigManagerUserConfig CreationClassName Description DeviceID DisplayType ErrorCleared ErrorDescription InstallDate IsLocked LastErrorCode MonitorManufacturer MonitorType Name PixelsPerXLogicalInch PixelsPerYLogicalInch PNPDeviceID PowerManagementCapabilities PowerManagementSupported ScreenHeight ScreenWidth Status StatusInfo SystemCreationClassName SystemName
C:\Users\Vikram>wmic path win32_desktopmonitor GET Availability,Caption
Availability Caption
8 LCD 1280x800
3 Default Monitor
It returns a line with column headers and a single row for each monitor you have. The column 'Availability' tells you whether the monitor is turned on or not. 8 means turned off, 3 means ON.
In the above output, I have an actual display LCD 128x800, which is off, and a virtual display called 'Default Monitor' (from Microsoft Remote Desktop) that is turned on.
You can get the full object as well, showing useful info like DPI, monitor size, etc:
C:\Users\Vikram>wmic path win32_desktopmonitor
Availability Bandwidth Caption ConfigManagerErrorCode ConfigManagerUserConfig CreationClassName Description DeviceID DisplayType ErrorCleared ErrorDescription InstallDate IsLocked LastErrorCode MonitorManufacturer MonitorType Name PixelsPerXLogicalInch PixelsPerYLogicalInch PNPDeviceID PowerManagementCapabilities PowerManagementSupported ScreenHeight ScreenWidth Status StatusInfo SystemCreationClassName SystemName
8 LCD 1280x800 0 FALSE Win32_DesktopMonitor LCD 1280x800 DesktopMonitor1 Lenovo LCD 1280x800 LCD 1280x800 96 96 DISPLAY\LEN4010\4&3A89619C&0&UID67568640 OK Win32_ComputerSystem DESKTOP-DNTB7R7
3 Default Monitor Win32_DesktopMonitor Default Monitor DesktopMonitor2 Default Monitor Default Monitor 96 96 800 1280 OK Win32_ComputerSystem DESKTOP-DNTB7R7