Do you specifically want to use the TV speakers when watching TV (not the surround sound)? If so, I can add that to the plan below. Are there any other devices (game systems, audio components, etc)? If you have a DVR, the cabling might be different (not sure how time warner works, but it can be different with DirecTv depending on the box you are using).
OK, let me see if I can do this so it makes some sense. There are 2 basic ways to hook things up. One feeds everything through the receiver and uses it process audio and switch video. The other passed video signals to the TV and audio signals to the receiver.
Option 1 - everything runs through the receiver.
Audio for all devices is played through receiver. Switching inputs on receiver switches the audio and video sources/pass throughs. Cables should go something like this:
coax from wall to IN on cable box
hdmi from OUT on cable box to IN on receiver
hdmi from OUT on receiver to IN on tv
Since it's a BD player/receiver AIO, you shouldn't need any cabling to address the BD player.
Set your TV's input to input used by the hdmi on the back of the TV. You'll never need to change this. Use the different inputs on the receiver to change between BD and cable. Something like TV/video 1 for cable and BD/video 2 for the BD player.
Assuming no universal remote, use the cable box controller to change channels and the receiver remote to control volume.
Option 2 - feed video to TV, audio to receiver
Audio for all devices is played through receiver. Switching inputs on receiver switches the audio source. Switching inputs on the TV changes the video sources. Cables should go something like this:
coax from wall to IN on cable box
components from OUT on cable box to IN on tv
digital audio (either digital coax or optical) from OUT on cable box to IN on receiver
hdmi from OUT on receiver to IN on tv
You'll have to change the inputs on BOTH the tv and the receiver based on what you are watching. The cable box will use one input on the receiver, the BD player/receiver will use another. Same for the receiver... the cable box will use one input, the BD player will use another.
Again, assuming no universal remote, use the cable box remote to change channels and the receiver remote to control sound.