The screen is black and power led is blinking green

why not get the service manual on it, and not guess.
?
this is LED TV and any board inside scan fail even the LED bank.
lacking the real manual how can you even check voltages?
ask sony for the manual yet?

perform the 'Flashlight test'
. LCD LED TV Repair No Image Blank Black Screen Flashlight Test How to Fix...

Seems that way. Fact that you saw the logo on screen eliminates the inverter board.

These blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices. Viewing it in "Mosaic" or "Magazine" will make surf easy.
http://electronicshelponline.blogspot.com/
Blinking codes details to many popular brand TVs are given. Surf the site with patience. Do a search by type in the brand name of the device to the search box.
Counting of number of blinks to Philips TVs is entirely different to that of other brand TVs. It is not a direct count procedure. The site have details about how to count the number of LED blinks [Fault Codes] to Philips brand TVs are given; along with details of the faulty circuit location.

Tv have power LED lights indication are blinking and recycle blinking.Mean the tv power supply board is the problems and the causes.That the board,where the power a/c cord plug into it.Tries websites like Shopjimmy.com,Ebay.com to buy a whole refurbish power supply board for the replacement.

Have you tried booting the machine into safe mode? turn off the pc and try inserting a rescue boot disc to see if it will go that route.

Call to Our Technical Support Number 1-800-204-4427 for PC Screen Problems and Get Instant Resolution of Your Query.

Hi..there,
You've got a busted backlight inverter... Need to replaced a new one...

Well, suddenly it worked again. But I waited the whole day >.>

I had this same problem and after doing some research, I removed the lamp, cleaned it and plugged it back in. It fixed my problem completely.