There is no other router it can connect to, because all other wifi networks in the area protected and no one knows their keys apart from their owners.
As for its own key, of course I can not be 100% sure the user entered it correctly, but shouldn't it be already stored in connman's settings? Because mine is stored (in plain text) in a configuration file that looks like so and is unique for each interface and network the interface has connected to.
Connecting to a different router creates a new file with similar name, but does not delete the existing one. I know that because I have deleted old configs a few times.
As for the log, if it had network access, I would grab one and study it before asking here. Unfortunately, the family can not tell the difference between a network cable and a phone one... and they only have one network cable, the one that connects the router to the pc.