Bravia NX720 55

It turned off and now it won't turn back on, light blinks 3 time

Since the TV is still receiving power, the problem is going to be with the TV's mainboard.  After you unplugged the TV and plugged it back in, you said the power light went out again, so I assume the standby light wasn't flashing again?  The flashing standby light is indicating an error code so my suggestion is to contact Sony for service options regardless if there is a warranty or not because service is the only solution to this situation.  Don't forget to provide them the error code or 4 flashes repeating.

I just worked on this last week 13 blinks means there is a problem with the backlights.So it can be 1 of 2 things bad inverter board( which costs less than $200) or the panel in which case you can thow the TV away as it will probably cost as much for a new TV.Unfortunately the set I worked on ended up being panel. If you try the inverter board just take your time removing it its plugged in rather tight I gently tapped it out with a screwdriver to get it started.

The TV Dude

Try leaving the TV unpugged for 30 minutes so the TV can reset itself.
If that doesn't work, most likely the TV has a power supply related problem. The most common thing to go out is the circuit board that supply power to the screen. Commonly called a Backlight Inverter Board.
I can't say it's 100% the problem because I can't actually look at the tv over the internet.
If by chance the TV is still under warranty, go that route.
If not under warranty and If you have some electronic experience, you can purchase a Service Manual over the internet and diagnose the source of the problem and fix it by soldering in the new part. The Service Manual will give you flashing red light codes, circuit diagrams, test points, and part# lists. Usually, cost under $20.

I hope I shed some light on the subject for you.

Are you sure about the 13 flashes. Error code only goes to 8 flashes.

I have the same problem, called sony up but they are not responding back. The tv is still under warranty and brought it from Amazon. My situation is same but my led error code is 4 or 5 flashes. Does any one knows what's wrong with it.?

I finally managed to solve this problem by unplugging everything - scarts - HDD cables - power etc and left it for an hour. When I turned it back on again the problem had sorted itself out.