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1998 Jeep Grand Cherokee Laredo issue

If the car sits without being used, the battery dies. I have changed the battery and made sure there were no battery issues, Changed the contacts, verified the alternator is working properly, gave it a tune up, no lights are turned on, removed the cig lighter, and turned off the switch that controls the interior lights to be turned on and the dashboard dimmer. The car also is consistantly not having a sharp instant start. There is a 1 second lag before it starts on 1 turn on the ignition.

ANY freaking ideas? Thank you in advance