You don't need good batteries in the fob to start the car. Hold one end of the fob right against the start button when pushing it in. Owners manual has instructions.
I struggled with that exact same stud on my Mazda 6, went through 3 or 4 bits and wasn't getting anywhere. Picked up a cobalt bit from the local store and it zipped through the stud in 30 seconds.
Something non rusting (stainless ?).
ENGINE AND ENGINE COOLING : EXHAUST SYSTEM
Number 10097841
NHTSA Item Number 01-025-12-2699
Date 2017-04-25
Summary Some vehicles may exhibit an exhaust leaking noise from the rear of the vehicle. The noise may be caused by a gap between the exhaust hanger...
"Try 50' of standard 14/3 extension cord, but left wound in a coil. Your compressor probably won't start.
Now, unwind the coil. Away she goes."
I hope you are kidding. Mechanical configuration has absolutely no affect on the flow of electricity. Measure the resistance of that wire coiled and...
There is also a tiny red button on the inducer that is an over temperature switch. Press it to see if it resets, or use a multimeter to make sure it is failed open.