It sounds like you somehow managed to bypass the tutorial step where you're given the transponder ability. That'd explain why agreeing to turn on the transponder fails; it assumes your fleet has that ability, but it doesn't due to somehow skipping that step. For the time being, I'd recommend restarting the tutorial and being careful to follow the instructions.
There are definitely some ways to get it off the rails, though how this in particular might have happened is a bit of a head-scratcher. The only way that comes to mind is not fighting the pirate fleet at the beginning and wandering off to explore the system instead. Might be worth approaching it as both a tutorial and a mission that can be failed.
Welcome to the forum, by the way
Removing the ability to move and having "PRESS F5 TO QUICKSAVE" be in the middle of the screen in big flashing letters, maybe some sound effects, would be good.
Hmm, that's a really good idea, let me make a note. Doesn't seem like it would help in this particular case, though. It's just fundamentally tricky to make it unbreakable, what with the sandbox nature of things. I guess it could do with a bit more hardening.