JP5 is a jumper that short-circuits across the power switch. It’s there for you to “hotwire” the circuit permanently on, for example if you do not install the power switch. If the circuit is not working without a jumper there, then it would certainly appear that the power switch is *not* working correctly, or has a bad connection.
Unless there is a scratch in the circuit board at just the right place, I don’t see any other way for this to be the case.
