I also found out what the solution is! On the mainboard (near the power connector) is a TI chip (Texas Instruments), identified as BQ 24740. (Texas Intruments part # BQ24740) This is the battery loader and power control chip. It is easily destroyed by a weak and flimsy external power supply, like what is delivered with HP products. The DE-soldering and soldering is tricky, because it is a QFN package, and very small. It solved my problem for just $ 8for the chip and $60 for a local shop to install