No sound. No Internal Speakers in 'Sound' window in Preferences

Late 2012 model A1418/2.7GHz Core i5 — installed 1TB SSD and 16GB memory. Fresh install of Catalina and migrated data from late 2009 iMac via Time Machine. Every time there was very good audio from the usual start up sound (which would indicate to me that the internal speakers are functioning well). In the process of confirming all files had migrated and checking functionality of everything, I noticed the speaker icon in the top bar was grayed out. Opened preferences, sound window — in the ‘Output’ tab there is no ‘Internal Speakers’ shown. Spent quite some time on line with Apple troubleshooting the issue. Tried finding and cleaning up some files to enable resetting and identifying the speakers — all to no avail. Took computer to local Apple store — they tried everything they could to resolve via software — no change. Next thing Apple said they would need to do is start replacing hardware (obviously too costly for age of computer). First thing they were going to replace was the logic board. Is there other piece of hardware besides the logic board that would have an impact on the unit recognizing the internal speakers? I’m sure the speakers are fully functional since the sound is quite loud at the startup sound.

Thanks

I forgot to mention -- tested output from headphone jack with plug-in apple earbuds - had sound but only on one channel, could not adjust volume. Tried battery powered external speakers that plugged in to the headphone jack -- relatively low audio on only one channel. Also tried USB headphones - no audio.