I have the exact same problem with out 2009 Edge Sport. It's only happened twice in the past few months and it's only when we leave the kids in the car listening to the radio with the engine off while we run into a store for a few minutes (~10minute battery drain.) A simple boost, no charging, allows the vehicle to start. Headlights, stereo, lock/unlock features all function, but attempting to start will cause the entire vehicle electronics to go haywire (CD/radio looses all of it's settings, info settings and mileage default back to factory settings.) I've checked the battery and alternator voltages and everything is fine when I get home to do so. I have noticed the battery positive terminal is very prone to corrosion/acid buildup and I cleaned it this summer when we first got this vehicle at 50,000km, and again after the first 'no start' episode and thought this was the cause. Vehicle currently has 61,00km. I coated the terminals and clamps with dielectric grease and the corrosion has not returned, but we had our second 'no start' episode last week. I don't want to buy a new battery without knowing that it is the problem.