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). It may have also been damaged in shipping.
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 simply return it to the store/retailer for a refund or exchange. You should be well within the return policy of most any vendor. While you could file a warranty claim with sony, that can take weeks or longer to get service and you shouldn't have to deal with a faulty tv right out of the box. The store should make it right for you.
My apologies for the news,