First, I usually don't say this but ..its a new boat, call your dealer. Even just speaking with them over the phone can be better than a chain of posts here.
Second, I assume it is a standard battery config. One motor and two batteries on a 1/both/2/off switch. The House 12V is connected to the motor start wire so it runs on the same battery as the motor, which is dependent on the switch position.
Typically people alternate batteries each trip or "out & back" in order to keep both batteries charged. Some people run the switch on BOTH to charge both. That is a dumb idea...but thats another discussion.
When the HOUSE12v is configured in circuit with the motor, a temporary sudden drop in voltage from starting the motor can drop out the electronics. This is because they automatically shut OFF if the voltage drops below a lower limit (10 volts generally). Isolating the House on its own battery is a better config...but thats another discussion.
Yes, new motors(the bigger ones) can have problems running if they don't have a battery connected.
The battery switches can fail and also the connections can be bad but you can't see them without twisting the switch around. Its not easy...see "First"
So, questions
Which position was your switch? To troubleshoot use the other position.
What do you mean by "power button"? Do you mean the motor Start button or the Red 40A breaker?
When your electronics shut off did lights,horn, pumps still work before you pressed the "power button"?
The most important question to answer is "What caused the motor to shut off?"
What is your skill/experience level with boats, motors, electrical?