Problem solved.
I deleted the config folder where I added the new trim reset after the recent update and replaced it with the safety folder (I save my config after every change).
And everything worked perfectly again: The engine started without problems the way I started it always.
Then I again added the trim reset (to the same button as before) and the engine start routine still worked.
I have no logical explanation for this bug besides "It's just DCS, what do You expect".
Thank You for trying to help me!
MiGCap1's post in Engine do not start anymore after update was marked as the answer