No sound from iMac except for the start up chime

I have seen many similar problems with this iMac. Just wondering if anyone else has my exact problem and may have a solution.

My iMac has no sound at all (except startup chimes) and no way of changing the settings in system pref's as it shows no alternatives to select other than "Digital out".

The previous owner has removed the headphone socket and cable leaving an empty socket on the motherboard. Does this need to be replaced to enable the internal speakers to work?

The obvious solution around "no internal sound" is just to airplay to a wifi speaker, but I would like to have my internal speakers up and running. Not worried about being able to connect anything from the headphone socket.

Thanks in advance of any help.