Electric Engineers and Thinkpad Geeks, help me with my Dead Battery

I bought a defect 4 cell X41 tablet battery from ebay. I need a new battery and thought it would be a nice project. So here is the thing:

I dissassembled the battery and the cells seemed to be OK. The batteries are in series connection and each of them shows about 3V charge with the multimeter (I went through the series and obviously got 3V,6V,9V and 12 with the last battery).

However, at the front connector I get nothing, 0V (leftmost panel connector is -, rightmost is +).
I finally found out that when I use the rightmost batteries + and the front panel connectors -, the multimeter measures 12V.
But for a reason I don't understand, when I connect the rightmost batteries + with the front panel +, the multimeter shows 1,5V.

Whats wrong here? Would it be insane to wire the front panel + to the rightmost battery? I'd get the current, but I have no clue how the battery charge/discharge and circuitry works. My reasoning behind this is that the circuit board may just remit the + from the rightmost battery to the middle of the circuit board, where it's wired to the front panel. And there could be a shortage in the middle of circuit board between + and -. I don't know if that's a stupid idea, but I'm not an electrical engineer.