Thanks for the replies.
1) What part of the home is the GFCI located in? Kitchen, bathroom, garage, outside receptacle, etc? What receptacles are located downstream from the GFCI?
2) Was there any recent electrical performed on this circuit prior to the GFCI not working? Any receptacle replacements, switch replacements, etc?
3) Any chance that you can obtain an AC voltmeter that has a built-in continuity testing feature from a friend or a neighbor?
4) I'm still not understanding what you mean? You keep mentioning that no power on the GFCI screws that screw down on the LINE wires. Yet you also mention the wires test OK. Not sure what type of tester you are using as it needs to be a 2 wire contact tester or an AC voltmeter?
I need to confirm if you have 120 volts on the LINE side GFCI wires from Hot to Neutral and from Hot to Ground and if 0 volts from Neutral to Ground. Do you measure 120 volts on at the GFCI LINE side hot and neutral screws with the LOAD side disconnected?
5) Is the branch circuit configured as a shared neutral circuit? Is the circuit breaker that controls the GFCI a single pole or a double pole breaker? Or 2 single pole breakers with a common trip handle tie?