The HP 11 Chromebook has a special battery with three cells and a protection circuit that will shut down when the cells drop below 2.5 V each or less than 7.5 VDC on the entire battery. I know because I am typing this answer on my HP 11 Chromebook, which had the same symptoms. I had to open the Chromebook to check the battery, and I did test each cell. I did a local cell charge on each and brought the up to 4 VDC for a total of 12 VDC but the protection circuit has a special chip (BQ30Z554-R1) that shuts down the battery. I searched for the specific chip and it has logic to do that, and there is no way to reset it, so my only solution was to buy a new battery . You can find the on eBay and it will cost less than a new Chromebook. If I managed to replace my battery, so can you.