Sounds like a loose ground, or even a positive on the battery. With all of the extra connections I have hanging off of my battery on both positive, and negative connections. I started the truck the other day, and it clicked, went dead for just a second, and then it was good. Truck started fine, and ran fine. Well in doing my e-fan upgrade Friday, I found a loose stud on the ground side of the battery. There was my problem. My connections have no corrosion. I grease my connections to prevent this. This would also make sense that they would have told you that the battery had been disconnected when it hadn't. If you have some corrosion, you can use some baking soda, and water mixed up about 2 TLBS to a glass of water, to dissolve the corrosion on the battery, the terminals, and the cables, then coat it all in grease to prevent future issues.
