Weird electrical problem

I have a 2000 Honda Insight hybrid that has been running great, but a very strange thing happened last week. I left the lights on one morning, draining the battery, so got a jump and drove it around to recharge everything (the big battery that is responsible for adding power and is what makes it a hybrid was also drained down to zero). This seemed to go fine, except that now what happens is that it won’t start on a first try anymore. If I turn the key to on (but don’t have to try to start it) the dashboard lights come on but very dim, then after a few seconds they get marginally brighter. If I try to start the car, it won’t start. But if I turn the key to off and then to on again, the dash lights come on bright (as they normally should, though sometimes this takes a couple on-off cycles) and the car starts right up and runs, everything behaving as if nothing was wrong, including the auto stop, where at a stop the engine shuts off after taking it out of gear, but starts right back up again when I put it back into gear. Seems like the strangest thing, and I cannot imagine what electrical thing might require this on-off cycling in order to get it to work. Any ideas?

It appears you have a intermittent, bad, power connection somewhere. It may be with the ignition switch or in the power buss. A faulty relay could also be causing the trouble. Try cleaning the battery connections also.

I would try charging the 12V battery with the negative cable off. Then load test the 12V battery. If it passes, connect the battery and run the engine at 2500 to 3000 rpm to reset the battery display. Also check the ground strap from engine to frame, they break down.