Unfortunately, the issues you are experiencing are symptomatic of an internal hardware defect, meaning 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 2008 model, that type of failure wouldn’t be surprising. These all in one type systems tend to be made with much lower quality parts than their "separates" counterparts, and seeing a service life of about 5 years max is normal.
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 main unit
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; if you're thinking about a do it yourself repair, you'll need to be comfortable and skilled with electronics repairs, which would require dismantling the set (removing the back panel of the tv), diagnostics with a digital multimeter to test voltages inside, changing out boards as needed, and possibly desoldering/removing and soldering/replacing capacitors (a common failure point). Unfortunately, there are no parts readily available for these units and all support is long discontinued.
If you’re considering repair at a local shop, you’ll find a typical repair to be around $400 for diagnostics, parts, and labor, assuming parts (used) can be found.
Realistically though, it's probably time for a new system. These units are not built for longevity and are not intended to be serviced. You can buy a brand new and updated system with a fresh warranty for the same price range as repairs.
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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