This would be my guess as well (not the ignition switch, that typically
has different symptoms!)

The so called TW sensor tells the ECU the coolant temp. If it fails and
indicates a warmed up engine, you will have enormous difficulty starting
it. It's a cheap part, and it is pretty likely your problem.

If you need to start the car, or want to verify that this is the
problem, use started fluid in to the intake snorkel while someone cranks
the car (don't touch the gas pedal, just crank normally). Once it
catches, use the accelerator pedal to hold the engine speed at 1800-2000
rpm. It's possible you'll have to restart a few times this way, but
after about 20s of running you will be able to keep it running with the
accelerator pedal. This will rule out the ignition system or an air
blockage etc.

Good luck,
Arthur