Sony KP-51WS520 won't turn on

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.

Hi,
10 times standby flashing indicates problem of High Voltage Protection and need to check following parts in Sony KP-51WS520 rear projection tv.
Q8014 or Q8013 have shorted replace along with R8051 on D Board
IC8005 is damaged (D Board)
Hope these info will help you. If you have no experience of electronics stuff repair then local tv repairman is an option to get help.
Thanks.

Try connecting the TV directly to a different wall outlet and check. If the issue persists, try power resetting the TV. Turn Off the TV and remove the power plug from the wall outlet for 1 minute and reconnect it and check the operation. If the issue persists, then the TV requires service.

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.

Google (understanding sony blinking codes) and up will come
the Blinking codes for sony.

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

Type in Sony Blinking codes on Google you will find all blinking codes and what they mean.

There is a small diode in the power supply that is bad. Do you have the capability to replace this yourself? (can you solder?) If so I can help you through it.

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.