Probably a little late on this one, and perhaps not helpful but...
Asd many have stated, most likely the connector for the external PSU to the laptop is damaged. Connectors often fail, since you're constantly plugging things in and out of it. If anyone in this thread has this problem, I would strongly advise to NOT route power via the battery connections. As the OP stated (quite rightly) there are several connections, including data, between the battery pack unit (which also has some intelligence) and the laptop.
Often laptops will check the part number of the battery, and refuse to charge it if it doesn't recognise it, or if its not deisgned to work with it. This not only ensures that the thing won't
explode when using a dodgy copied battery (by over charging) but also, so companies can make more money, forcing the consumer to use one specific battery, and charging (punn intended) what they like for it.
Replacing the DC/AC jack on a laptop isn't always easy, but it can be done, with basic tools. The only really hard part is getting to it. Laptops have many tinys screws which are easily lost (my laptop has lost 13 so far lol). When desoldering parts, remember, you usually have to sacrifice something. That is either the PCB, or the component.
In this case, the DC jack is screwed and so you must sacrifice that, as you obviously want the PCB to be fine. Instead of trying to desolder it as-is (difficult on a double sided/multilayer PCB, with non-lead solder), cut it off. destroy it with wire cutters, leaving only the pins stuck in the board. These can then be easily removed with a soldering iron, just don't 'pull' or 'push' them, melt the solder, and tap them until they come out. Any force could lift/break the copper pads on the PCB (which are held on with glue which melts at a lower temp than solder), and make your life a lot more difficult. Clean it up with soldering wick and flux, leaving pristine tinned pads, and solder on a new one - which you can usually get form ebay
Done this 4 times with my laptop, and 5 times with its singe USB socket. It's still going, although I should probably stop dropping it on its side at work.
Its not an interesting 'hack', but its less likely to destroy your laptops ability to communicate/power from batteries. - which defeats the point of a 'portable computer', as well as leave you wil NO way to power the thing.