I believe the socket has finally broken. The computer no longer sees that the power cord is plugged in and the battery is not charging. The socket feels loose. I have several other dell laptops in my laptop graveyard and am wondering what DC sockets off what other laptops would be compatible so that I can swap them out. I have the hexagonal plug and cord and would rather keep that since I have 2 of those power supplies already and don't really want to replace them.
The jack on this model is part of a daughterboard that's unique to the 1545:
You can see if they have the hexagonal version, but there weren't many of those shipped relative to the number of systems built - the vast majority take the round barrel connector.