Circuit worked briefly after replacing GFCI, but stoppped
Non-contact voltage tester can be squirrely but assuming it's working I would do the following.
Make sure the GFCI is reset. With the faceplates removed start at the GFCI and carefully contact the hot lead on the line side of the GFCI. If it shows hot go to the load sign and do the same. If that is hot continue downstream checking each outlet until you isolate the problem area.
Once you do shut down the breaker and check the connections. Since you've had several issues with wires disconnecting make sure that you're not using backstabs - they are unreliable. Use the screws and always wrap the copper around the screw in a clockwise direction. I would also suggest that you pigtail your outlets. Don't through-wire them.
That should help you zero in on the problem It could be a bad outlet but it's probably a loose connection.