What happens if it's plugged into the system and the system is turned on? Black screen? Garbled output? POST beeps from the BIOS? Do any of the outputs work or none at all? etc...
Also, in which way did it fail? Was it continous degradation or a sudden failure?
There are a lot of things that could have gone wrong here, for example a bad power supply in the case, frying the graphics card on-board power supply.
The thermal grease is non-conductive, they wouldn't have used conductive grease right next to a row of supply caps
The first thing I'd do would be to check supply voltages with a scope. Anything beyond that may be difficult / impossible to diagnose and repair due to the sheer complexity of the device.