How do you determine good charging? You are probably using the charger supplied with the HT. Did you measure the voltage of the batteries? Could there be an internal contact problem with the batteries? Does it have some internal backup battery which is most likely not a reason for not powering up. It is really strange that all four of them should have the same problem. That's why I am looking at the charger.
Sound thinking with Occam's Razor in hand.