No signal to PC screen

What do I have left to do when I am not getting an image on my screen? I have the traditional desktop personal computer. Last week it has worked smoothly but on shutting down I heard the screen making some flashing sounds.
I already verified the connections to the graphics card with correct screwing the two bolts on the blue screen plug. I removed it, cleaned it, verified that all pins are in correct positions and put it back. Still I am getting a blinking power led on the computer screen when the Central Processing Unit is booting up.
I would love to have another computer screen to verify if my screen has gone down but another screen will not be available to me for the time being. I prefer some quick diagnostics to know which parts have gone wrong for I want to change for only the damaged parts in my PC.
