Does not come on.

Sounds like you have a shutdown condition in the power supply section.Your gonna need a service manual a vom and possibly a good scope. Theres not much you can do as too look at it and see a bad part. And theres not alot you can check staticly without a service manual. Although there is a common problem with this chassis as were in some of the older models of sony.. the Horizontal driver transformer as well as the regulator ic has a cold solder joint on them. Good luck

Additionally, the number of times the LED blinks is a code as to what the problem is specifically.

First, you have to grab your tv remote then press:

Power, 5, VOL (-), Power

Self Diagnostics screen should come up.

That is as far as I got. I don't know how to interpret these codes.

If anyone can help me any further, it is greatly appreciated.

I have KV-27FS320 and my diagnostic screen looks like:

   2: +B OCP         0
   3: +B OVP     N/A
   4: V STOP         0
   5: AKB              0
   9: ZCD           255
101:WDT           N/A


--
Thanks to Ron Purkisher and Dave Wreski for getting me this far. (http://www.iwaynet.net/~nesda/SonyBlink.html)

First, you have to grab your tv remote then press:

Power, 5, VOL (-), Power

Self Diagnostics screen should come up.

That is as far as I got. I don't know how to interpret these codes.

If anyone can help me any further, it is greatly appreciated.

My diagnostic screen looks like:

   2: +B OCP         0
   3: +B OVP     N/A
   4: V STOP         0
   5: AKB              0
   9: ZCD           255
101:WDT           N/A


--
Thanks to Ron Purkisher and Dave Wreski (http://www.iwaynet.net/~nesda/SonyBlink.html)

This is what you should do, call Sony TV techs 1888,989,7669 give them the model and serial number then tell them how many blinks, they will suggest IC-numbers on the Silicone board, See if you can locate them, its is a commen problem they already know about it, then before u hang up as for the part number then u can cross refference the sony part number with the accual part number. They will give u numbers then u have to figure out what they are maybe its on the part itself if u can make it out. Then find a parts distributor and replace them. Most likely the parts range from 6-12$ just becareful with the board, make sure u dont break of any small resistors. Or if ur not really tech savy should take it to a local service tech