Neutral and ground connected together and/or
Disconnect the neutral wire from the load side of the new GFCI and check for no continuity between it and the ground wire.
Reconnect the neutral.
Put a 7-1/2w incand. lamp in series with the ground wire that serves the cable downstream of your GFCI.
If the voltage across the bulb reads from 0.6 vac to up to 120vac you've found your leakage path to ground. A normal reading would be less than 15 mVac.