Unfortunately, the issues you are experiencing are symptomatic of an internal hardware defect, meaning a faulty 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).
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; at that point your best recourse is to return it to the store for a refund/exchange.
My apologies for the news,