99 Toyota Camry No Crank, No Start

Hello! I’m looking for some help on my Camry. So a
couple of weeks ago I started to have some
problems starting my Camry. In the mornings it
would take at least 15 minutes to start the car.
During the time I would turn the key and it wouldn’t
crank or start. Once the car is started it ran fine for
the rest of the day and if I stopped somewhere it
would start right up. A couple days ago it wouldn’t
start at all. I changed the battery and it started. I
took it down to Autozone and rest the battery,
starter, and alternator. All checked out fine. The
tech did mention that the alternator is overcharging
the battery. Well yesterday the car won’t start even
trying to jump start it. I changed the starter, starter
relay, alternator 100a fuse, with the new battery and
still not starting. AAA was able to start it using a
wire to the battery and start and I was able to drive
for 50 miles with no issues. However, once I turned
off the car it won’t start again. Any suggestion on
what the issue might be? Thank you!