Infiniti i35,died while driving and then after jump started the windows were going up and down on their own, windshield wipers and radio turning on and off on their own. went to o'reillys had them test everything they said the alternator and everything was fine except the battery. Bought a new battery then 2 days later it died while running and hen we cranked it the engine sounded like it wanted to start but couldnt, then after a acouple of minutes of tightening the terminals and cranking the engine on it worked. next day i went to start it and have it running the a/c while i was finishing getting ready and it died. jump started it and let it run for a few minutes, seemed fine then about 2 miles later the gas pedal went out while it was still running

 

This is a strange problem that I've never heard of before. Check the main chassis ground located under the battery. Follow the negative battery cable down under the battery tray to find it.

 

Can be an intermittent problem with the alternator (brushes may be at the end) and when tested it showed ok, like my daughter I35, try to tap on the alternator to see if the spring pushes the brushes a tiny forward. You can also try and measure the charge your self with a multimeter.