Just so its clean in my head
You are not getting anything on your screen when you turn on your pc?
Have you tried testing the monitor itself? On a different system that is known to work. When you say you can turn your computer off, do you mean when you press the power button again it does not turn off?
*This is not great for the hard drive as it could be accessing data at the time* BUT you should be able to turn your computer off by holding the power button down for 5 secs (ish) That "should" turn it off straight away.