This old model had poor protection for the underlying logic board if liquid got into the keyboard. I once opened one up and found blue-green crystals all over the logic board, crystals that gave off a feral smell. Turned out the person's daughter (the user) had a pet ferret who liked to run across the keyboard... and she did not realize that ferrets pee as they run. It had sprinkled her keyboard over and over until the unit shorted out. That was just ... nasty.
Pull the RAM chips, and check for corrosion on the connections – a sure sign of further liquid damage. Those old white MacBooks were a giant pain to work on for anything more than a drive swap, battery replacement, or RAM upgrade, and are worth less than a tank of gas these days. My Opinion: The repair isn't worth it. Pull the drive, save the data, and advise them to get something newer. Doesn't have to be new – not all of us have that money – but something within the last 6-8 years. Perhaps you even have such a used unit already that you could sell them?