Thank you for trying,
unfortunately, that really leaves only the possibility of a hardware fault, meaning the rear receiver unit has an internal defect (bad power supply, bad radio, etc)
This issue could be a manufacturing defect, but is also often caused by a power event (shock/surge, prolonged over/under voltage condition, etc).
This could also be the result of age related wear and tear, as a 2005 model, that type of failure wouldn’t be surprising. This type of fault is the biggest downside to these all in one theater systems, as some component inevitably fails and the entire system has to be replaced. All of the components are proprietary to this model and cannot be replaced individually. They are also not feasible to fix - there are no parts available and labor costs alone would be more than a whole new system.
At this point you could certainly continue using it as a stereo (front speakers only) system, otherwise replacement will be the most economical option here.
Personally, I do not recommend these theater in a box systems, as they tend to be short lived and low quality components. You'll get far better performance and features, and often lower upfront cost, from a "separates" system, meaning a standalone amp/receiver, individual speakers, and separate bluray player.
If you are pinched for space though or prefer the budget model systems, there are some soundbars that would work well for you. I can recommend some replcement options for you, or help find a repair shop if you prefer, depending how you'd like to proceed.
Best regards, ***** ***** for the news,