Are you sure the cells are functioning properly? Did you test each individual cell or the whole pack.Even with one faulty cell inside the pack will put the charging in safe mode and will not charge .
Same thing happened to me with and HP Envy Ultrabook 6.Replaced the pack and everything was fine.Opened up the old pack and found one cell was dead and it would not take charge and the rest were all good .Only takes one cell to put those packs in the trash heap.Such a waste.
edited for better explanation.
Battery packs ,specifically Lithium, are designed in a series parallel configuration. Lithium batteries charge fine in parallel but not well in series.So the pack is charged by splitting the parallel cells from the series cells .This is called balancing.Theirs a PCB inside the pack that does this.The charge controller detects how those individual parallel batteries are charging and switches them accordingly.If it detects that one parallel set isn't charging correctly it goes into safe mode.This is a safety feature built in to prevent fire by charging bad batteries.