Panasonic TC - P4251 42 inch light blinks 12 times won't power on.

These blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.
http://electro-medical.blogspot.com/
Blinking codes details of many popular brand TVs are given. Surf the site with patience.

the number of blinks will determine problem area.

That is a error code and depending (Panasonic?) on model means either power board or another issue---the error codes can sometimes be misleading or too vague to pinpoint to one board.

Note: these (all brands) sets only sell boards, no individual parts.

Not knowing your skill level you may be able to tell me that, the first thing would be to examine the power board for damage or puffed up filter caps---let me know if questions here etc.

4 blinks Power SOS P Board.

Visit the site named 'Electro-help' for more details. Click this link. View it in "Timeslide" option, which can be selected from the drop down box menu by the [Sidebar] tag, at the top left corner of the display window. It will make search easy. There are more than 1000 posts to different brand TVs now. Pull up older posts there.

12 blinks Sound SOS H Board has the fault. Replace it. For more details, visit this site named "Electro-help'. Check this link, and select the site named above. It has details about this fault.

Before going OFF, the standby LED might blink. These blinks are fault indication. The number of blink should be counted. Count the number of blinks at one time, before the TV goes OFF. [eg: 4 blinks Power SOS P Board; 6 blinks Driver SOS 1 SU / SD / SC Boards
(SC energy recovery circuit)] and so on. you can get more details from this site named 'Electro-help'. You can reach it by searching the keyword "electronicshelponline" by internet.

Y-Sustain board should be suspected. For more details, visit this site, named 'Electro-help'. Type in "electronicshelponline.blogspot' to your browsers' search box, and click search. It is a blogspot site in English Language. Sometimes, ads related to each post might help you to get details about the availablity of spare parts and price.

Power supply or related to it.

10 blinks check sc board for a short circuit in the mosfet ,replaces SC board

thought I would post this here for everyone.

1 blink STV 5v sense DG Board

2 blinks 15v SOS D Board

3 blinks 3.3v SOS D Board

4 blinks Power SOS P Board

5 blinks 5v SOS D Board

6 blinks Driver SOS 1 SU / SD / SC Boards
(SC energy recovery circuit)

7 blinks Driver SOS 2 SU / SD / SS Boards
(SC floating voltage area)

8 blinks Driver SOS 3 SS Board
(SS energy recovery circuit)

9 blinks Panel Config. SOS

10 blinks Sub 5v SOS / Main 3v SOS DG Board
DTV 9v SOS / Tuner Power SOS

11 blinks Fan SOS PB Board

12 blinks Sound SOS H Board

13 blinks Communication error DG Board
with IC8001 (Pesks Lite 2)