My 97 Toyota Corolla sometimes has trouble starting. Occasionally when I turn the key nothing (and I mean nothing) happens. When the key is turned all the way there is power in the car (lights, wipers, etc.), but it never even cranks. Sometimes if you hold the key turned all the way for several seconds it will start. Sometimes it starts right up with no problems, but about once a week it won't start at all. If I wait some undefined period of time (usually a few hours), when I come back it starts right up. This seems to be unrelated to temperature, time of day or when I drove it last...just random.
I took it in to the dealer and they said the battery connections were corroded. They cleaned them and it seemed to be better for a few days, but then I started to have problems again. I looked at the terminals and the positive one had more corrosion, so I cleaned it very well, but I continue to have problems. Any ideas?