Well, there are two possibilies:

1. The unit is defective.
2. There really is a ground fault some where.

Everybody wants to glom on to the first. It's certainly the easiest to check for ($14 or whatever for a new GFCI).

The second requires some intelligence. The first step is to remove the wires from the load side of the GFCI. If that allows the GFCI to reset then you do have a ground fault downstream. First unplug everything that is plugged into that circuit and reconnect the load wires.

If that doesn't help, you're going to need to start unhooking the circuit at various places to see if you can find it. Most likely culprit if there are no actual loads is that the ground and neutrals are touching somewhere. Inspect each box to make sure that isn't happening. I'd almost always start with the exterior receptacles. They tend to take a lot of abuse and water.

Newer GFCIs wil not reset without power being supplied to them.

Mae sure the breaker is on.