Those all in one systems are not really possible to fix yourself. You're gonna have to contact samsung, see if you're still in warranty, and see if its worth it to fix it.
A janky workaround might be to borrow a cheap DVD player from a friend, and see if you can hook it up to the AUX, D-IN, or some other audio input on the back of the old broken home theater DVD device. This MIGHT allow you to get sound from the new DVD player through the old sound system. No promises though.