If the RCA connections on the back say "output" then you could make a connection from there to a stereo systems "AUX" input (or "TV" in if your stereo has this) Now you would be able to hear the TV sound from your stereo speakers. If no stereo near by, then you either chuck the set out and buy a new TV, or go and buy a stereo system with speakers. Some TV's (not many at the 27" size)have speaker jacks on the back to enable you to hook up external speakers. If your set had these it would be worth trying a pair of small speakers, but try first, the sound issue could be from the TV's internal amplifier which would mean even from external speakers the sound would go bad.
The sound on my TV has gone bad. What is the simplest and cheapest way to hook up a speaker and by pass the TV speakers? It has no headphone jack, but does have the RCA audio plugs. It is a 27 inch Daewoo and has a great picture, but after it is on for an hour or so the sound becomes muffled and bad. Maybe I should just chuck it and get another?