I had the same problem and found a solution - or found out what was actually the problem.
First of all let me say that it is not the CPU or the harddrive!
I tried un-pluggng all the cables and re-plugging it all back in again - but nothing worked.
Then I pressed the on-button on the monitor and held down the Auto button which is also located at the bottom of the monitor screen.
I had a menu option that said 'repair windows environment' 'advanced option' 're-start windows' etc.
I chose to 're-start windows' - this restarted the computer but I still ended up with a black screen.
So I repeated the above process of pressing Auto and on-button, menu came up. I selected option 'repair windows environment'
Then after loading and 2 screens that flashed - I got a black screen with white writing, a little down the screen it said something like 'repair windows environment' and then a count down timer in seconds. This option is a waste of time as there is nothing wrong with Windows. I selected the next option down 'start as normal' and pressed enter.
My screen was back!!
I closed it down and re-started it to see if it worked. Black screen again!
So then I started to adjust the cable head - the part that is plugged into the monitor.
First time it did not work but I did see some light flashing so I continued adjusting then pressing the on button on the monitor and suddenly it came on, I could see my desktop icons.
I am having this problem a lot now and have to always adjust the cable head - so I think it must be the cable.