The low battery warning and non-charging is like the Surface's version of the dreaded bsod ... I left my work SB3 charging for 2 days via the awful dock and came back to .... nothing. Wouldn't start, wouldn't charge. Tried the comical Msft suggestion to flip the SB upside down and reconnect it but needless to say that didn't work. I guess it wasn't a full moon....
Eventually it fired up but seriously, the SB3 is a total piece of cr*p and Msft has no more business being in the hardware space than in the internet space. They are a desktop software company struggling to remain relevant and frankly failing miserably. If this SB3 wasn't a work machine I'd dump it in a heartbeat.
Try the battery driver uninstall, as I said earlier that worked for me and it's been perfect since then. By the way, there's no SB3, hasn't even been announced yet.
I think there is a SB3 and some microsoft employees have them... perhaps the poster is one of them ;)