Installing GFI problem
I am optimistic that what you are seeing is exactly as KUI****G described, a "ghost voltage" on the long neutral/ground runs. To a neon test lamp or sensitive voltmeter this leakage current will appear as a voltage. Actually, it is leakage current as a result of capacitive coupling of the neutral and ground wires to the line wire. This current is so small that it is completely harmless and consumes no power.
You may wish to prove that it is a "ghost voltage" and not a short, here is how: Make a tester out of a 4W or 7W incandescent night light to use in place of your neon tester. This will completely suppress the "ghost voltage" and the lamp should only light on the black wire.
When installing the GFI outlet, take the time to read all the instructions, they are quite good and necessary.