Please help with getting 5.1 sound from my TV!

Hi, and thank you for any help you could provide. My audio system, as is probably obvious, is the Sony DAV-HDX500 Bravia DVD Home Theatre System. My TV is a Sony KDL-32S3000 Bravia LCD Flatscreen Digital Color TV. My Blu-Ray player is a Sony Playstation 3. As you can see my entire home theater system is Sony-made, so I figured they should all be compatible. Apparently I was mistaken. Basically, I want to be able to watch Blu-Ray disk movies from my PS3, with 5.1 surround sound from the Home Theatre System. Problem is, there's zero audio coming from the Theatre System! Here's what I've done so far: Plugged the Theatre System into a power source. Set up and attached all speakers plus subwoofer. Attached the Theatre System to the TV via HDMI cable (it's a $100 Monster HDMI cable, so I'm guessing it should work. It says it outputs uncompressed 7.1 audio, and I'm using a 5.1 system, so it should be fine, right?). Went to the Bravia TV, set the HDMI CONTROL to ON, and set the Audio output from "Speakers" to "External Speakers". Went to the Bravia Theatre System, set the HDMI CONTROL to ON. Also set the AUDIO(HDMI) to ON. Hit FUNCTION on the remote control until "TV" came up. Went back to the Bravia TV, changed it to TV mode. Silence. Went to the Bravia TV, set it to the HDMI port which feeds to the Playstation 3. Popped a Blu-Ray Movie ("300") in. Silence. Obviously, silence from the TV's two speakers, but silence from the 5 speakers attached to the system! Also, silence from the subwoofer too. I've turned the TV on and off. I've turned the Theatre System on and off. Turned them BOTH on and off. No luck. Now there's one thing I haven't done, and that's attach the Red/White audio cable (mainly because it's not sold with the system, and I don't have one just yet). Is this cable required for an audio signal to go FROM the tv TO the Theatre System? The HDMI cable, then, will only carry audio FROM the system TO the tv? If that is the case then, well, I feel rather silly. However I'd rather feel silly for a little, then feel silly for a lot and having spent $300 on an audio system that doesn't output audio. I can say, however, that definitely, the 5 speakers plus subwoofer are all WORKING, because I connected my XBox 360 via component cables to the Theatre system, then the Theatre System via HDMI to the TV. Then I turned on the Xbox and put Halo 3 in (I chose Halo 3 because it's a game I know outputs in 5.1 sound). As expected, the sound emanated from all the 5 speakers plus the subwoofer. I disconnected all but one, then reconnected them one by one, just to be sure. The five speakers definitely work, they just won't output sound from either the TV, or the PS3 (although the PS3 isn't directly connected to the system, but it shouldn't have to be right? If the PS3 is connected to the TV via HDMI, and the TV is connected to the system via HDMI, and the TV is set to output its audio from the external speakers ... shouldn't that work?) If the Red/White cable is required for any signal from the TV to the system anyway, then I have one further question: does this audio cable carry uncompressed 5.1 data? If not, then that's a bit of a bummer because the 5.1 digital sound from the Playstation 3 will get compressed on its way to the surround sound speakers, but I suppose there's nothing I can do about that. Finally: if all I really want to use this system for is its 5.1 surround sound, and not so much for its DVD-playing capability (because I also own a PS3 AND an Xbox 360, both of which also serve as DVD-players anyway), then it isn't necessary for it to take up the HDMI port, right? I only have two HDMI ports on my TV, so HDMI-space is limited.