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We had a GFCI on garage, it "controls" a few yard/garage outlet, sunroom patio light, two bathroom wall power outlet and a build-in shelf light of living room. Last October, during our roof was replaced, we found out water got into the metal wire pipe of sunroom patio light, and the GFCI cold not be reset. So, I replaced the light and its power switch, the GFCI can be reset, those power under its "controls" was back on.

The wired thing is: when I tried to push GFCI back to its socket (see picture), the GFCI jumped the power, then it CAN NOT be reset anymore, so those power under its controls was off again. I thought the GFCI itself has problem due to its age (~20 years I guess), I bought a new one and replace it (see picture), it could not solve the problem, GFCI could not be reset. I thought I should fix its problem after replacing the sunroom patio light and switch because water get the wire and connection wet.

Please advise what could be the problem of this GFCI, any easy fix? Thank you !

Make sure that the grounds and neutrals are not touching (and that the neutral is not touching the box or other metal. Also make sure you've got things on the right screws. The wires coming from the panel should be connected to the line side, the wires going to your other receptacles should be connected to the load side. Get this wrong and you'll have problems.

Finally, if all that seems fine, make sure that you don't still have a ground fault. The first step is to disconnect the wires going to the line side (your other receptacles won't work but at least the receptacle itself should work and reset). If that works and reconnecting the other wires works, you'll have to debug further along in the circuit.

Ron, thank you so much for detailed suggestion, I will go through these very carefully. I had a digital multimeter for Amp/ Volt, I could use it somehow to detect "ground fault" if there were any, right?