You have a basic setup that is 1 zone that is 7.1 surround, and then 5 rooms of distributed audio.
As a rule, the first thing you want to do is get really organized. That means that every single wire coming out of the wall gets a decent label on it which you can read 10 years from now. Also, put together a spreadsheet for the little details.
The cable with 4 wires coming out of the wall is industry standard. You have one cable, and the four conductors handle a stereo speaker pair in a room. It is likely 16 gauge or 14 gauge wire and it will have printed on the side '16/4' or 14/4' meaning the wire is 16 gauge with 4 conductors. This runs from the head end (where all the equipment will be) to the volume control in each of your five stereo zones. This is extremely common to see, and I fully expect that you will find that there are five 16/4 wires coming out of the wall... One for each of the stereo zones. Then the rest of the 2-conductor cables will be for the 7 channels in the TV room, and there should be one coaxial cable for the subwoofer. If this is NOT what is there, then you need to respond with details of what is there.
I would also pull off a volume control at some point to see if anyone was bright enough to wire some cat-5 to each of the volume controls so an actual controller could be put in place. Doesn't sound like it from what has been said so far.
If the setup is 7.1 + 5 stereo zones, then I would do what was said to begin with.
1. Get a surround A/V receiver which has enough inputs and power for the main TV room area and is at least a 7.1 channel, 2-zone product.
2. Get a decent amplifier for the distributed audio speakers (the 5 stereo zones).
3. Get a good 6 room speaker selector with integrated impedance matching.
Any sources you want to play into the distributed system must be connected with analog audio connections (red/white RCA jacks). While this seems easy enough, certain new products don't have analog audio connections on them anymore! Things like AppleTV fall into this category. They only have a digital optical and a HDMI connection on them and at this time, no receiver, to my knowledge, will decode audio off of HDMI to a second zone, so you will need to address that with us later if you run into that issue (there are some new solutions which help with this!)
So, let's use the Denon 1911 previously mentioned as an example.
1. Connect your cable box to the SAT/CBL input on the back of the receiver via HDMI.
2. Connect your cable box to the SAT/CBL input on the back of the receiver via red/white RCA audio connections.
3. Connect your Blu-ray Disc player to the BD input on the back of the receiver via HDMI.
4. Connect your Blu-ray Disc player to the BD input on the back of the receiver via red/white RCA audio connections.
5. Connect the rest of your sources in this manner. Any sources which do not need to feed into the distributed audio system do not need to be connected via RCA cables.
6. Connect your 7.1 audio speaker wires to the red/black 5-way binding posts on the back of the receiver. Use decent banana plugs to do this properly!
7. Connect the red/white "Zone 2 Output" RCA jacks to your dedicated whole house amplifier.
8. Connect the whole house amplifier outputs to the input connection on your speaker selector
9. Connect each pair of speakers in your whole house system to each of the audio outputs on the speaker selector. One speaker pair per output pair.
Turn on stuff/test/enjoy
Option 2 follow all the same advice, but instead of a speaker selector and a single amp, get a 12 channel amplifier with audio loop through.
Niles SI 1230 Systems Integration 12 Channel Power Amplifier 760514007376 | eBay
A model like this provided 30 dedicated watts to each speaker in the entire system and should do so reliably.
NOTE: Make sure all your amplifiers are in a well ventilated area. Do NOT put them into enclosed cabinetry unless that cabinetry has proper ventilation running through it.
I do have a preference for multi-channel amplifiers as I've had great luck with them and like the dedicated power. But, I've set things up with a single amp without issue as well.
I don't like the fact that the previously linked Dayton amp has a fan on it. I don't believe that fans should be on consumer grade equipment as it adds noise to the room that equipment is in. IF the equipment is in a separate room, such as a basement storage area, then this won't matter at all, but if the whole house amplifier is in the TV room, then when the fan is on, it will add noise to this room which is something I don't like. The above linked Niles amplifier is convection cooled, so there are no fans. But it must be well ventilated to suck head away properly.
