I have multiple systems that coincidently have unrecognizeable power supply problem. Purchased new battery per Dell, didn't solve problem.
If I purchase a docking station PD01X will it charge the battery given it bypasses the normal adapter?
I do know your post is quite old. Just in case it would help!
"unrecognizeable power supply problem" is often related to a faulty power connector or charging circuit on the motherboard. I just suppose you have already checked that your power adapter woks fine.
So most of the time, plugging a PC with such faulty motherboard will power the PC bypassing the faulty connector or circuit. It will thus charge battery. It has always worked for me, it should for you.
Kind regards from France