Hi swsiefken,
First try to use another input like your DVD player to confirm if the fault was came from the TV itself. If the symptoms remain the same in all inputs, this is an indication that the fault was came from the TV.
Check the earphone jack, hook up your headset through this jack and check if you can hear the sound.
If yes, then the fault is between the earphone jack or the internal speaker of the TV. Check the speakers' resistance using the multimeter, you can get 8 ohms reading if the speakers is rated 8 ohms and you can hear a crackling sound upon testing. If the resistance is higher than 8-16ohms, this is an indication of faulty speaker. You have to replaced it with new one.
If you confirmed that the speakers are good, replaced the earphone jack with new one or if you have an electrical contact cleaner, spray it directly to this jack.
If no sound, the fault is in the audio circuitry in the main board, fixing this board is quite technical because the parts are surface mounted and too small. If you are going to DIY, I would advice you to replaced the entire
mainboard for your convenient because no soldering required replacing this board.
Hope I helped you.
Have a nice day!
Thanks for using Fixya.