Video Game Console Repair Questions? Ask a Technician ASAP
Hello and Welcome. My name is Michael.
Technically you have done everything you can do on your end, the next best and cheapest advise is to find out If one of your friends might have the same console, take the balance board and try syncing it with their console. Doing it so you will accomplish:
1- know for sure if your balance board went bad totally coincidentally.
2- by syncing it with another console it will override the bad syncing connection produced with your own console.
Some people would rather reset the whole console back to factory settings re-syncing every device for the first time, BUT that's a high price to pay to erase every progress of every game ever played, especially if the balancing board ends up being defective anyways.....so think twice before doing this last resort move.
Please let me know if there is anything else I could help you with.