If you are comfortable with a screwdriver, and a volt/ohm meter, find out what outlets are on the circuit, turn the breaker off. Pull all of the outlets out of the boxes. Disconnect the black and whites from the GFCI outlet. Using the continuity setting on your electrical test meter, see if there is any "continuity" between the bare ground and any white or black conductor. If you get "continuity" I'd recommend that you remove the outlets black and white wires and do the same scenario. It is possible that the bare wire is touching or coming in contact with the white wire with in the device box. If the bare was coming in contact with a black wire, the circuit would trip. What nobody has advised you about is how a GFCI device works. Think of it as a sink if your faucet fills the sink up with a gallon of water, the drain should see a gallon leaving. This works the same way with electricity. The current has to enter the circuit and leave the circuit equally. If some current "leaks" to ground, there is an imbalance in the circuit and the GFCI device is doing it's job correctly by tripping.