I have the same issue - out of warranty (it was extended to 3 yrs for this manufacturing defect, their service agent said this in so many words - MANUFACTURING DEFECT!!)
They cant do anything though since its out of warranty. Said I should dispose of the device carefully as battery could explode - can you believe it.
You are right - MS should stick to software and not make any hardware. Though I did enjoy the SP4 a lot and funnily enough its still working perfectly. I wish they could get their act together and follow up with good customer care and replace the device. I even indicated that I am happy to pay for a replacement at a discounted price.