It certainly isn't the fan because it does spin and there is no display.Check your Fan of the Graphic Card and If it is not working. Clean the fan and Try again.
Well, the card was working fine the otjer week, but now it wontDid you try changing the display output? and coil whine doesn't mean that the graphic card is broken a lot of graphic cards has coil whine in them and people use them just fine it doesn't mean that your component is dying coil whine is harmless.
I get a post code (keyboard error) when the gpu is not in the pc, but with the gpu in I get no beebs at all.Well, can you try it on another motherboard and cpu? if it didnt work try changing your power supply for testing and see if it works, if after all of that it didnt work just buy a new graphic card.