Check to make sure that the emergency brake pedal hasn't been pushed down at all. I know that for about the first year I owned my '93 I would always hit the pedal when I got in. It would set off the chime and also the lights on the dash.
Not really sure about the stalling while driving, but it would be a good idea to start out with removing the cables from the battery, removing the boots and cleaning the cables VERY good. Our cars are quite picky when it comes to elecrtical connections at the battery.