With a black screen but the monitor working means the computer has not turned on. In this case Your problem is probably the power supply on the computer tray, not the hard drive. You can repair the supply ( capacitors dry out and bulge in the power supply ) or replace it with a new one.
When capacitors dry out they need to warm up before they work Untill they finally fail. I fixed one of these game box power supplys not too long ago.