Unfortunately, the issues you are experiencing are symptomatic of an internal hardware defect, often a faulty power supply or main/control board, though there are many possible failure points. 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 unit is well past its service life at this point and has greatly exceeded any value that could be reasonably expected of it.
There is one step you can take here, both as a possible fix, as well as a diagnostic evaluation:
1) Unplug the power cord from the outlet
2) Wait at least 1 hour (60+ Minutes)
3) Press and hold the power button (on the set, not the remote) for 60 seconds
4) Keep holding power button while plugging back in, and for another 60 seconds after. When plugging back in, go directly to the wall outlet, bypassing any power strips or surge protectors.
If this reset process does not work, it would unfortunately confirm an internal hardware failure.
This is something that would require repairs to correct; though repairs simply aren't feasible. There are no longer parts readily available and labor alone would greatly exceed the value of the system.
If you’re considering repair at a local shop, you’ll find a typical repair to be around $200 for diagnostics, parts, and labor.
For a stereo of this type/age however, replacement will make more sense. You can get a brand new model with updated features and a fresh warranty in the $100-200 range.
Depending how you’d like to proceed here, I can help with finding parts, finding a repair shop, or recommending replacement options. Just let me know.
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