How to troubleshoot breaker/electrical problems?

Sounds like a broken or corroded neutral. You are not using a volt meter that will give you a numerical reading are you? Is the terminal on the buss bar damaged, burnt or corroded? Also are there 3 way switches involved? Also check the main breaker for that panel and see if 1 leg is tripped on it. Check breaker with ohm meter in on position 1 lead to the wire screw other lead to the snap prongs for buss bar. If good you will have continuity