You may try opening up your case and checking the resisters on your graphics card. The resistors are the things that look like little towers. If the top of any of them or bulging, ruptured or just missing altogether that could be the issue. If a resister has fallen off and the PC remained on for a long period of time it may have fried the buses or damaged the card itself, in which case you will have to buy a new card.
Another thing to check for if you are using a card that has it's own cooling system (a.k.a. cooling fan or custom heat sink) is to check that cooling mechanism. I had a VC burn up in an older machine because the cooling fan built into the card stopped working and the card overheated and fried. If it is using a heat sink, make sure the sink is still firmly attached to the card and is not loose or god forbid, fallen off.
If you are STILL having problems and none of the above seemed to be causing the problem, check the prongs on the external cord connection. If they are bent or broken or are not aligning with the holes in the card properly, that could also cause an issue. If that is the case you can just go to Fry's and purchase a new $5 cable.