Are there any volume controls in the walls associated with the 4 in-ceiling speakers?
Are the speakers all in different rooms or are they in a single room?
There is NO CHANCE there was a TV in place when they were using speakers. This was not part of a surround sound setup, but was used for background audio in the home using a piece of crap amplifier (which they took with them) and some crappy in-ceiling speakers. This is LOW END builder grade crap. The fact they didn't leave the amplifier, but left the phoenix connector which the amplifier will need to connect is a pure sign of stupidity on their part. Really f'd up to take with them.
So, you have what appears to be a setup using series/parralel wiring out to a single zone of audio, all playing the same source at the same volume. If there are no volume controls, then you wouldn't have separate volume control for the four sets of speakers. All speakers will be playing the exact same audio.
If I were looking to get some audio out of the speakers for background music (nothing surround sound or TV watching here!!!) then I would pick up an amplifier on eBay. If there are no volume controls, I might look for a volume control/speaker selector as well.
The Niles SSVC-4 (speaker selector/volume control/4-room) is about $100, though I bet there are some generic models for less money.
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ie: Pyle for $50...
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Pyle is not nearly the quality of Niles, so you get what you pay for here!
Then you need an amplifier. The amplifier will provide power to run all the speakers. I often pick up some used Niles, Sonance, or similar better known brands.
Something like this is a good price...
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So, you are under $200 doing it this way with decent components. Make sure they aren't packed into a tight closet or you will suffocate them.
Hook up any audio source you want. Like your phone, a FM tuner, or a Bluetooth receiver. Maybe pick up a Sonos (a few hundred $$$), or hook up some other audio only streaming device. You will need to provide an audio source for your setup, but this will get you going right near your budget.
Realize that builders have ZERO F'N CLUE HOW TO DO HOME AUDIO!!! So, you didn't buy some kick-arse system. You got shafted here... pretty bad IMO.
But, hey, you have some speakers, so you might as well put them to use. $150 is about all I'd want to spend if that was the setup I was stuck with. But, once it is playing, you will still be pretty stoked I expect.