2007 Mazda 3 Car will not turn over

I can't get the car to turn over. I get the exact same results as I would if I would try to start it without the clutch. The battery and alternator are both less than a year old. I am able to start it only by push starting it. I've taken it to a mechanic 6 times and they are shrugging their shoulders. The mechanics have been unable to replicate the problem.

The clutch is fully pressed. The key is fully turned. The car is in neutral.

Problem in the morning (cold). Problem after commute home (hot)