2009 JAGUAR XK Engine Problems

PARKED IN THE GARAGE, SOMETIME FOR A FEW DAYS OR THE NEXT DAY, THE CAR WILL NOT START ON OCCASIONS. NO SLOW STARTING OR CLICKING OF A BAD BATTERY, JUST A HUMMING THEN NOTHING. NO REASON FOR THE FAILURE. DOESN'T ACT LIKE A LOW BATTERY. I CHARGED THE BATTERY, AND JUMPED IT WITH NO SUCCESS. AFTER SEVERAL ATTEMPTS I WOULD GO INSIDE AND RETURNED IN 30 MINUTES OR SO,TRY AGAIN; SOMETIME IT WOULD START. AFTER SEVERAL TIMES, IN THE PAST TWO YEARS, OF THE CAR NOT STARTING I PURCHASED A NEW BATTERY; SAME THING. I DO NOTHING TO REMEDY THE PROBLEM, OTHER THAN WAIT A BIT AND TRY AGAIN. MY ONLINE RESEARCH SHOWS THAT THIS IS HAPPENING TO OFTEN. MANY PEOPLE HAVE THERE CAR TAKEN TO DEALERSHIP AND THEY FIND NOTHING. IT JUST STARTS WITHOUT ANY SERVICE, AUTOMOTIVE REPAIR SHOPS AND DEALERSHIPS COULDN'T FIND WHAT CAUSES THE ENGINE TO FAIL...