TV will not come on. TV standby light blinks nine times continuously. TV is Sony KP-51WS520

Is the light blinking 9 times? If so thats a very common problem caused by failed diodes on the G board which will need to be replaced.

Standby flashing light shows that tv got some internal problem. How many times standby light is flashing is info that provide info about what section of tv got problem.
Count standby light blinks and let me know, there would be 3 seconds long pause in blinks so count pause to pause.

Count the number of blinks of the standby light. It will bink a count, pause and do it again (Common counts are 2 -9) Give this count to a Sony service center and they can help you know what the issue is. (Probably the lamp)

Ck small blue capacitor next to hori output Transistor 2k volts they have been known to go Bad, if its OK replace Both of your STK ICs STK392-110s use 180s Mats has them 1-800-628-1118

Replace the G board ( where the power cord plugs into)

Something bad in power supply or horiz output.Possible bad gun.Needs a repair shop unless you know electronics.

You need to call a Sony service center for this problem. It will cost you less in the long run.

You need to check supply volts on main micro IC702 on main board of Sony KP-51WS520 TV.
If you have experience of big TV repair then I would recommend to get service manual of TV from any online store and check above said IC supply volts. TV must give error by blinking light in case any problem in drive circuits and if main micro fried, no error signal will be there.

When a Sony TV flashes five times, that means that there is an AKB circuit fault.
Six blinks is also a fault related to video problems, and regards a fault concerning the digital board and the Jungle IC (the main CPU).

This means that there is something wrong with the video.
Try first unplugging power for few hours, if that does not work, call a technician, as several IC and components must be tested and eventually replaced.