Recharging fails, but the fault is not with the battery or the AC power supply.
The battery that came with the refurbished computer I accidentally ran down to 0% according to a Linux app or 1% according to BIOS and the BIOS said it was performing normally anyway; recharging never raised it. I've tried recharging a large new battery (9-cell) with the computer on and in use for about 8 hours, with the computer on and with the lid open but not in use for about 3 hours, and with the computer powered off for at least 8 hours and none of these attempts made any difference; before recharging the charge was never higher than 65% according to the app or 66% according to the BIOS and after trying to recharge it remained at 0% according to an app or 1% according to the BIOS and, according to the app, charging and, according to the BIOS, performing normally. The small replacement battery (6-cell) started at 77% according to the app and 76% according to the BIOS, which is the opposite of the readings of the other batteries. Altogether, I tried three batteries, at least two of them new. Charge levels never rose, only staying level or dropping, according to the BIOS or a Linux app.
I tried two power brick-and-cable sets with the same output voltage (one borrowed from another machine). The results were always failures.
The BIOS reports the existence of a second battery bay (I don't know where that bay is unless there's a dock that I don't have) and reports the second bay as empty, so it seems to know the difference between lack of battery and having no charge.
Now, some weeks later, the battery is probably dead and the BIOS doesn't see it.
So the fault is inside the laptop, somewhere between the AC receptacle on the back of the laptop and the battery connector visible only when I remove the battery. I don't know the computer's history. What should I fix or replace?