Regarding the motor: the crank shaft position sensor might be dying.

This happened on my 2007 4.8, but not exactly like your scenario. Basically, the motor would crank and crank until I lifted off the brake pedal (when trying to start it). Then, after a few more tries, the engine finally fired up. I immediately drove it out of the parking garage and into the lot, where I shut it off and let the tow truck come pick it up. The verdict was two sensors, one of which was the crank shaft position sensor. With this, I got a transmission malfunction error message, but the transmission checked out OK. The other sensor escapes my mind at the moment. I have the paperwork if you're interested.

With these vehicles, one minor electrical issue (such as a bad battery) can cause all sorts of symptoms that aren't really issues. The ripple effect of bad programming.