The juice for the lights and other 12 volt accessories should be running from the alternator when the engine is running. After you've cleaned the battery post, charged it to capacity and whatever else need to be done to it and if it's still not working; I'd start by checking the alternator output and see what voltage you've got there. My alternator quit on me during a trip and it caused similar problems. I cranked the generator, plugged in a 50 amp charger to the battery to make it home. I took the generator out and went to an alternator rebuilder and had it repaired for about $45. It had a bad resistor or something like that. At any rate, it was 3 or 4 times less money than a rebuilt one.
