I'm going to reiterate the battery cables again. My daughter's PT Cruiser was killing batteries about every 3-4 months. No warning, it would start fine then the next time she went to start it, no click nothing just completely dead. I finally bought an OEM set of new cables and viola, haven't had that problem in over a year. If nothing else, it's cheap insurance. Not sure if you can get OEM cables for either of the engines for the 1st gens, so you may have to make them yourself or find a shop that can fab new ones using your originals as a template. All this being said, I have yet to take my own advice.
As for the lamp, yes it still sounds like a ground.