From the information you've provided, I'd guess the following - Leo is right, get an amp (7.1) to bring all the inputs (tv, skybox, dvd etc.) and send the sound out to the ceiling speakers (and get a separate subwoofer).
For example, what I have
All inputs go via hdmi cable into the amp (I've a Sony STR-DH800, but there are newer ones/ other brands out there). Talk to the guys in Richer Sounds on Boards.ie, they have good products and good advice (no affiliation) . I have the tv, skybox, xbox, blueray, chromecast, and record player all going to the amp.
You can set up the speakers, well some of them anyway, to act as surround speakers, but get a dedicated subwoofer for the base, and maybe a central speaker for the front of the telly for dialog. It will take a bit of research to come up with the optimal solution. Read up about 7.1 surround sound etc.
Also, TV speakers are normally not the best, simply because of the constraints of getting them into a tv housing. Some TV channels, and all dvds will have at least 5.1 surround sound so it is worth it.
And check the make a model of the speakers in the ceiling, to see if it is worth it at all, and as Leo said, placement is critical for surround sound.
I don't know about the BOSE 3to1. Is that an old record player/tape drive (with built in Amp)? If so, then chances are it doesn't have hdmi outputs. You should be able to connect into one of the inputs in the Sony amp, but the question is, is it worth it? If it's only for the record player, then there are new, reasonably priced record players out there.
I'd suggest a bit of research in your near future. Ask me any questions. I may not be able to answer them, but I have gone down the same path before.