After i paused a movie, my sony bravia KDL55EX640 55" LED tv had a black screen & will not come back on.

Your TV could of had stopped working and you need to by a new TV.It would be more cheaper to by a new TV than to try and fix the TV that is broken.

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?

chip failure

LCD Easy Fix (sound but no picture) - YouTube

? 4:52
https://www.youtube.com/watch?v=IBRE1Dcyxp4
Jan 13, 2012 - Uploaded by Clay Whitehead
TV Has Sound But No Picture Troubleshooting Guide - Duration: 2:30. by Repair.com 467,264 views. 2:30. LCD & LED TV Repair - No Image ...

How to fix sony bravia has black screen - Digital TV - Streaming ...

www.tomsguide.com/forum/56867-4-sony-bravia-black-screen

Aug 19, 2014 - 12 posts - ‎11 authors
Hello, My Sony Bravia TV screen has gone all black. The green on/off light comes on,but no picture appears. The model ... Your solution solved the non picture for live tvbut still no picture (just sound) fir OnDemand. Score. 0. No picture on LCD TV with HDMI cable plugged into ...
5 posts
Aug 4, 2014
Tv problems picture ok but no sound - HDTV
4 posts
Sep 8, 2011
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Using the remote, open the system menu and reset the tv.

you need to change the picture board/ the display board

SONY BRAVIA 55EX720
2 lights blinking.

Hello,
the error light sequence that you are seeing is indicating a "backlight error". Most likely you have a bad inverter board -the board that powers up the back-lights behind the display panel. They might be available via ebay if you are a DIYer, or you need to call for sony service.
Good Luck!
Rich Lilja

Try going into menu input set up on tv and switch to av input. Just a thought I have the same model and had exact problem. All I had to do was change input style to av cable.