To rule hardware in or out, two quick tests.
Wiggle the plug while something is playing. A crackle, or sound appearing briefly, means a mechanical problem — a worn jack, or debris. Jacks fill with pocket lint remarkably fast, and a wooden toothpick and compressed air fixes a surprising share of "dead" headphone sockets.
Boot something else. A live USB system, or another operating system if the machine dual boots. Working there means the hardware is fine and the problem is entirely software on the original system. That single test saves a lot of guessing and takes ten minutes.
If it is silent everywhere, including in firmware beeps and in another operating system, then it is the jack or the board.