Your VGA can be broken, but before I state that, I have a question for You!
Did You try to blow the dust out?
If You did and it's still not working, buy DVI or VGA cable and try to use them. It can be a problem with your HDMI port in Your VGA.
Hope it helps!
VGA? VGA = NOT the graphics card, do not confuse things.
Do you have another monitor or TV with an HDMI port. Try to connect other devices to your GPU
and see how that turns out.