The following test is based on the fact that the neutral is supposed to be isolated from ground EXCEPT at the main disconnect service panel.
Turn off the circuit breaker, disconnect the circuit neutral at the panel, and then measure the resistance between the hot and ground, and between the neutral and ground, with whatever other equipment that is on the circuit switched ON.
The test will tell you if either the circuit or any equipment on the circuit has any leakage to ground. You should have at least 1,000,000 Ohms resistance, and ideally it should show an open circuit on the highest scale of your ohm-meter.
If you find low resistance to the ground wire or the ground terminal of a grounded receptacle, then you have a leakage path that will trip a GFCI.
You can try to locate the fault by turning off each piece of equipment to see it that solves the problem. If that doesn't fix it, then unplug the equipment one at a time and check to see if that causes an open circuit to ground. If it is still not an open circuit to ground with all equipment unplugged, then you have a neutral or hot lead (probably a neutral) that is grounded and you need to search to find that ground fault.
If there is an open circuit with everything unplugged, then reconnect the neutral and turn on the breaker, and try again to reset the GFCI receptacle. If it still trips, then try replacing the GFCI receptacle.