I'd suggest buying a cheap multimeter, it'll make diagnosing the problems a lot easier. If you're using the dash and we assume it's accurate, and we also assume the new battery is in top nick: The voltage when it's running is what you'd expect so I'll guess the generator/regulator is working however the dash won't tell you if it is or isn't charging the battery. The voltage when it's off isn't ok so I'd say you have a problem with either the earths to the battery or the power lead from the battery.
