I've been cleaning up an Atari 400 that had a bad RF cable, and cleaned the machine thoroughly so it's looking great. It's working well apart from the keyboard, where most of the keys aren't working: some columns on the far left work (Q, A, Z and W, S, X) but almost everything else doesn't, and backspace even acts like reset.
Is this likely to be an issue with the membrane or is it more likely that there's some cracked solder joints / faulty components on the main board? Is there a good way to test and diagnose the keyboard outside of the machine?