I have a Yamaha RX - V665 and the right rear surround works only part of the time.

That can only happen I think if you have the speakers connected to the wrong terminals. Check the connections and make certain they are right, plus the wire is good and not touching any parts it shouldn't

go to audio set up and configure the system for 5.1 or higher sound output.then only all the speakers ll work

You need something like this:

Digital to Analogue 5.1 converter:
http://www.ebay.com.au/itm/like/131104197505?limghlpsr=true&hlpv=2&ops=true&viphx=1&hlpht=true&lpid=107&chn=ps

I have never used one of these before, but i have worked in the audio industry and if this device works as advertised it will suit your needs.

don`t open it yet

check ur speaker wires, try disconnect all wires from back of unit and then try to turn on unit .
if it stays on whit no wires attached than u have short connection at speaker wires .
if doesn`t come on then try to fasten screws at back of the unit ,
may sound like BS but if amp board don`t have good ground connection it can go in protection mode happened to me on RX-V592

Simple web searches get answers faster than waiting for one of us to pick up the question.

Try "Yamaha RX-V665 manual"

Why does impedance concern you? This receiver can be configured for loads as low as 6 ohms. The front speakers can be 4 ohms if you use a single pair.

It's all explained on page 106.

This receiver should be able to drive most quality speaker systems. Anything from ub/satellite sets to 6-matched speakers plus a sub will work. It seems you have a choice already made for surrounds. Whatever yoy choose, you have to balance performance, aesthetics and price. The Yamaha is probably not a limitation. Get what you can afford and place to your satisfaction.

The volume keys should be working by default, but you may have volume punch through turned on (meaning the remote is sending signals for TV or CABLE volume function no matter what mode you are actually on). To unlock volume control for AUX mode, do the following:
1. Press and release AUX
2. Press and hold SETUP until the remote blinks twice
3. Type 993
4. Press and release VOL-
The remote should blink four times to confirm unlock.

What do you mean - code? It's hardware, connect it via its optical digital cable.

You may find a solution by doing some of the things I have tried - see below

I recently puchased this model to replace an older Yamaha system that also had this shut-off problem. The new RX665 system has the same problem but I check the impedance setting using the instruction in the manaul anyway. The problem persists. I have check all speaker wire to make sure nothing was touching. I did find one wire touching on the center speaker but the problem persist.

Since the problem followed me when I moved and with a new amp, I am beginning to think I am have a speaker that's causing this - maybe the sub.

If your tv has an audio out jack attach a rca cable from that to your receiver any audio input.