[Scott Douglas]

I ran into a similar problem with my in-law's Lexus just the other day. Checked the car out one day and the next it wouldn't start. I was in the midst of checking it out the following day when my father-in-law got home, jumped in the car and started it before I could stop him. Battery showed 14V+ when running. I chalked it up to bad ignition switch possibly.
They called the other day with a no start again. This time the battery measured 10v.
I put in a new battery and problem seems to have been solved. No telling how old the old battery was.
I'll bet your battery has shorted plates and the second connection of the battery charger burned that connection out so it started.
I'd get a new battery in there as a first step.