That's novice advice (You risk electrical shock doing this) It has some truth but for anyone with electrical measurement/supply experience they won't get shocked. I am an EE and have been debugging electrical circuits for 50 years.
I have a similar problem and would like the pinouts for all the connectors involved with the battery subsystem.
There is a pair of connectors between the (1) Power adapter and the Dell body and another pair between the (2) battery and the Dell.
The (1) connectors have 2-3 (?) pins and the (2) connectors have 9(?) pins.
I have 1 new battery for the Dell. Also 3 older batteries that I would like to do a power charge/discharge cycle on them to check/improve their state.
I would like to charge the battery externally (Adapter to Battery) as well as check it's charge state.
I have taken apart one U1223 to check it's insides and it has 8 cells for 4300 mah. There is room inside for 2 more cells. I presume one can put in new 10 high capacity cells to get 6600 or 7800 mah for the unit.
Because the AC adapter output is 19 volts and the battery is 14.8 volts I wanted to know the pin out so I could devise a voltage divider to charge it external from the laptop enclosure. I later determined that the problem was because the female connector contacts were not contacting the pins on the laptop socket because of careless insertion and removal as well as stress during normal operation. The charging system is now working properly and I appreciate the interest.