There is one more possibility in addition to the suggestions already posted. I
came across a similar situation last month, an older GFCI just kept tripping
with nothing on it. This occured after I had shut off the circuit breaker for
awhile. Replacing the GFCI with a new one did no good. I finally traced it to a
loose wire on the breaker that feeds that circuit. The hold-down screw had
worked loose and the wire was barely touching, a bad situation.

Dennis