Broken audio jack is soldered to the motherboard
My audio jack is busted it wobbles and doesn’t connect. I think its pins are shot.
If your laptop’s motherboard has bent or broken pins, see the Motherboard Has a Bent or Broken Pin problem page for information and tips.
You did not tell us what manufacturer and model number it is.
If you are handy with a pencil soldering iron it can be replaced.
If you determine the age of the board and the total replacement say eBay has one. Compare this with a repair shop cost. You may ruin your board by removing the plug.
So if you are ready to do this your self, many boards have the same plug. A junked computer could be the source of a used plug, or a repair shop throwing away a non-working board.
There is a product for removing solder that looks like abraded copper, on a small roll. This has resin in the braid and you hold the braid on the solder joint spots and touch the soldering iron on the braid over the spot. The braid sucks up the solder leaving the spot empty. On the old board experiment first. Most plugs have the electrical connection and then two or more metal tangs thru the board to mechanically hold the plug more solid than just the wiring spots.
It is worth it if you want a project to enjoy. It is not easy and you may want to just replace the board or purchase a USB thumb device that can be used for your music/sound.