iMac built-in speakers won't work.

Is there something plugged into the iMac's headphone jack?

To check, go to Apple > System Preferences > Sound > Output.

If it is showing External Headphones for Output, then

1. something is plugged into the headphone output port
2. you have a jack that is busted off inside of the headphone output port
3. you have a stuck or a busted micro switch inside of the iMac's headphone output port

I am getting you moved to the iMac forums. However, you need to post more details to get fast help in this setting where helpers can neither see nor touch your computer.

And remember, iMacs have been min continuous production since 1998 in easily over a thousand variants! Saying 'It's an iMac," does not drive troubleshooting and resolution forward because different varinats have different configuations.