Am I correct that you only purchased the set 3 months ago brand new? Also was it from an Authorized dealer?
Have you checked the outlet (not sure what you mean exactly by power supply), with another device to make sure the outlet has power?
Also, are there any signs of life on the TV at all (buzz or hum, click when power button is pressed, or power cord is plugged in)?
Please disconnect the set from AC power for 2 minutes, then upon plugging back in, press and hold the power button for 8 seconds to try and force a reset.
If the TV still does not power up, then the flashing light would indicate that there is a short inside the set stopping it from fully powering up.
It is most probable that there is a failure on the power supply board inside the TV. Commonly the capacitors on this board will receive a surge and then fail. They can sometimes be visually verified by removing the rear of the set and inspecting them for bulges or leaking fluid at the top or the base of the caps. This is the most common mode of failure for these sets.
Seeing as you are barely into owning the set, you should contact the retailer and ask them where the closest service location is to have the TV repaired. I wish I had better news, but there are no buttons you can press to fix this and the TV will require service at this stage.
Did you try the reset?
If so, and it still didn't work...then sorry, and I wish I had better news for you.
You have a one year manufacturer's warranty on the set, so yes they will repair this for free for you.