The external battery port does not supply charging power. (Neither does the built-in battery circuitry on rev D 4000s and all 4000Ts, which is why non-rechargeable lithiums are installed by default). The internal battery on my 4000T has been dead since before I got the machine in 2004. I'm now on my second external battery pack, replaced about a year ago.
This is what I'm using now.
