replace the starter lets isolate all start components except the starter. Disconnect connector at the starter and hook up a direct connection jumper 12 gauge wire to the starter side of the connector. Run the wire into the engine compartment, turn ignition key to dash light up position and start the engine by a direct connection to the + batt post with the jumper wire lead. Some minor arcing might occur but if a firm placement on the post to problem, release when started. This will bypass all circuits in the car and check the starter action. Hook up a VOM at the batt to check the voltage drop when starting. Also check the amp draw if you have the meter.
If all checks out but since you are having start problems and now it seems to be working that intermittent issue check the ignition key switch at the column.
Might take a couple days to root it out at least you have a temp way to start if stranded.
