Thanks for the reply. I can feel the motor trying to move the cart, which is why I believe the motor is turning. I have removed the motor, and the spline looks ok on the motor. I'm assuming the spline would be disintegrated, and that I'd see lots of metal filings, which I'm not seeing. Before I start taking apart the differential, how would I make sure that it's not an electical problem? I had already charged my 3 year old batteries (after almost a year), and kept tabs on the process, which seemed very normal (high initial current, slowly dropped to near zero over the course of several hours). The connections all look clean, no corrosion, all are tight.
I had backed out of the spot where I park it, and it worked fine. Then, I put it into forward, and that's when the problem started - very suddenly. I found an exploded view of the differential, and was going to check the input shaft next. But, I dropped the differential pan, and found some filings but not the amount I would expect to find if one of these large gears had failed. Given that, it made sense that the hub spline failed, but they're not turning. Very perplexing.