I have the same problem. My Z830 is 3 yr-old. With power plugged in, the battery LED is lit orange, battery status says "99% available (plugged in, charging). It never goes to 100% and as soon as I unplug the power, the laptop shuts down immediately.
I don't mind paying for a new battery if needed, but just not sure if it will fix this problem.
So I had this problem for the last week, and have just solved it for an Inspiron 15z 5523 laptop. In my case, I had 4 orange flashes, then solid white. Everything including the bios was telling me the battery health was fine, and that the battery was also fully charged, however every time I unplugged the AC power cable, the laptop wouldn't draw power from the battery and would turn off immediately, and wouldn't power on again either until the power cable was plugged in.
I took the laptop apart, and after 2 frustrating days I noticed a miniscule switch located on the motherboard called "BATSW1". It was in the "off" position. I flicked it on, and now everything is absolutely fine. I don't know how the switch ended up in "off", but hopefully this will help someone. I've included an image of the switch.