I had a very similar problem.
Another symptom of mine was when I had my key is postion 2, only half of my warning lights would come on (the ones in the bottom of my gauge cluster).
The cause? The brushes/regulator unit. It takes two seconds to take out, you don't even need to jack up the car (if you're skinny, and can shimmy). Its on the back of the alternator, you just need a phillips screw driver to take it out (but a phillips socket on a 3/8ths rachet would be better - it'll probably be pretty stuck). Take it out, examin it, clean it, then try it again... If it still doesn't work, replace it. If its still the origninal alt. then it'll need to be replaced soon anyway. Its only a 20 or so dollar part, so no big deal if its not it, at least you've worked it out of the system. Its probably the cheapest common failure on these car$.
If you're lazy like me, doing this is much easier than checking all your connections
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