battery seems to be "cooking" when I put it on charge.

Hi,

Does the battery have the correct HP part number?

The following is taken from p.45 of the maintenance and service guide for the laptop.

8-cell, 2.55-Ah (73-Wh) Li-ion battery for use in all countries and regions except Japan 493976-001

8-cell, 2.55-Ah (73-Wh) Li-ion battery for use in Japan 534057-291

Sounds as though there is either a faulty battery or a problem with the laptop’s battery charging circuit.

Given that the charger runs the laptop OK, i.e. it hasn’t damaged any components in the power supply circuits to the laptop by having higher than stipulated voltage output, it appears that it is OK.

Nevertheless it may be advisable to test it anyway. Here’s a link that shows how to test the adapter. Scroll down to find the AC adapter test procedure.

Does the laptop work OK on the battery only?

If so and if Win 10 is installed, create a Win 10 battery report to check the status of the battery and check what it says

Sounds like your battery problem. Did you check it by changing your battery?