Stall while driving no crank/start

My car starting stalling
ooccasionally at lights and
itvdid it the other day and now
won't start. There is no cranking
or clicking noise when I turn key
in start although I hear
movement and feel something
move. I tried to jump start it.
Voltmeter reading on battery
was 12.4 or 12.6. Someone (a
mechanically inclined
friend)said it was most likely the
crankshaft position sensor. So I
changed that still nothing. So I
get it towed to a garage. They
call me and say its the starter. I
ask, "how do you know" they say
cuz that is what it usually is
when this happens. I ask didn't
they test things to know for sure
and the guy said well we won't
know if its the starter until we
replace it. So I say do not touch
my car. So I am back to trying to
figure out how to figure out what
is wrong before spending
anymore money. So I have it
narrowed down to the ignition
switch the starter solinoid or the
starter itself. I have a test light
and multimeter. I bought a code
reader but it said no codes
stored. I dont know if that is
because i had took all the
cables off the battery to make
sure they were connecting.
Every now and then my key
would be hot. Also while my
sister drove my car earlier that
day she took off in the low 1
gear amd cycled it back up to
drive while going 45 mph so I
am wondering if it coyld be
nuetral safety switch but tried to
start in nuetral and no crank.
Also tried some crazy
instructions from manual at
resetting the switch to no
results.  I hope I am not giving
too much info. Also a couple
months ago i took the battery
out of my car key cuz it was
causing alarm problems but i
dont have a start button on key.
Can you please give me some
advice? There has got to be way
to know for sure and i would like
to start with the simplist ways if
possible. Thank you.