I would tend to start with the most basic things first, especially since it seems you have a ton of electrical problems all at once. It sounds like you have had the battery out already, but I would make sure both battery connections are clean and firmly tightened.
Then I would trace the negative lead from the battery to wherever it attaches to the frame and/or the engine. At this point I'd remove the ground and clean that connection completely with sandpaper.
Next I'd trace the positive lead and make sure it is firmly attached to wherever it goes.
Hopefully it will be one of these basic things. If not, come back and post what you did and have found so far, and we'll try to suggest more things to try.