I have a GFCI in my garage that was working, but now won't catch at all. I pulled the downstream circuit by disconnecting the load wires and it still won't reset. I have 120 to the GFCI itself. I replaced the GFCI with another and have the same issue. The LED that's on the unit isn't lit. The power comes from an underground wire that's connected to a breaker out on my power pole (don't know if that matters).
If the GFCI won't reset, and there's nothing on the LOAD side of the GFCI (nothing plugged in, nothing on LOAD terminals). And you've replaced the device, with the same results. It would likely mean that either the device is wired incorrectly, or the line feeding it is damaged or wired incorrectly.
Modern GFCI devices will not set, if they are not hooked up properly. Make sure you've connected the wires feeding the device to the LINE terminals, and that you've connected all the wires properly and securely.
Make sure you read the manufacturer's instructions, as the light on the device means different things to different manufactures. Sometimes a light is good, sometimes it's bad, and sometimes it depends on the color of the light. A sure fire way to know if the device is set, is to measure the voltage at the receptacle.