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Wierd & Frustrating!
My long-distance analysis is that the battery is discharging to ground whether the ignition swtich is on or off -- I know you've checked, but that is nonetheless what I think.
You can check the situation at the battery with a multimeter with a current setting ($10-20 at Radio Shack).
1. Disconnect the battery's ground terminal.
2. Charge the battery if it's drained.
3. With the ignition off, put the positive multimeter lead on the battery's negative terminal, the negative multimeter lead on the ground strap.
4. I would expect to see a few milliampere's flowing (to run the clock). Anything more than that and I would conclude that the battery is not at fault, and I would start checking wiring to try to find what is grounded that shouldn't be -- and maybe vice-versa, because bad grounds also make crazy things happen.
Another possibility is that the battery light bulb in the instrument cluster is burned out, in which case the alternator will not put out any amps. If the light goes on when you turn on the ignition, you can dismiss that possibility, too.
Good luck
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jds
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