If your home theatre package has the same kind of video connection that your TV has, then yeah. What kind of video inputs does the TV have? It's probably just the RF cable and a single composite cable, I'm guessing. So the video would probably be the composite video cable from the player/receiver to the TV, and the audio would go from the player/receiver directly to the 5.1 speaker setup.
If there is only the cable coming out of the wall, and into the back of the Sylvania: Plug the cable into an old VCR. You can set up a VCR to surf your cable channels, send the picture to your Sylvania(thru the yellow jack), and output the sounds to the new home theater(thru the red & white)
Does the TV have red/white "audio out" plugs? If so, connect these to an input pair on your Phillips.
If it doesn't, are you using a decoder set top box from the cable company? If so, it will have a pair of audio output plugs. Connect these to your Phillips.
If you don't have either of these I'm afraid you're out of luck as far as listening to TV through the HT. That's because it has to be after the channel tuner has done it's thing and your HT does not have a tuner.
But does it work for DVDs? Can you see the DVD picture and hear the DVD audio through your HTiB? The setup I described should work for DVDs, but for everything else, HTiBs can be a bit limited. They don't accommodate a variety of inputs the way that home theatre receivers do. Which HTiB do you have? How many inputs does it have, and what kind of inputs does it allow?
Without knowing the specs on your HTiB, I'm guessing that if you want the sound for cable TV to come through the HTiB, you have to do one of two things:
You can do the following if your TV has audio *outputs*: RF cable from the wall into the TV, then red & white RCA cables from the TV into the HTiB.
2a. RF cable somehow going into the HTiB. I have no idea if HTiBs can accommodate an RF cable; I suspect they don't.
2b. If you're using a set-top box for cable, then the RF cable would go from the wall into the set-top box, and then either red & white RCA audio cables or a digital coax/optical audio cable to the HTiB, and also an S-video cable or single composite video cable from the set-top box to the HTiB. Again, I don't know if your HTiB can accommodate all of this.
Geez . . . now *I'm* starting to get confused. I don't think it's possible to listen to cable TV through an HTiB without both a set-top box and appropriate inputs on the HTiB, but hopefully someone more knowledgeable than I will chime in with a suggestion. But it would still be helpful to hear about what inputs are available on your HTiB.