You need to count the number of blinks between the pause. Most common is 9 blinks. Also- after you press POWER, do you hear a "click" or not? If no click and 9 blinks, you probably have a "zero detect circuit failure" and have two options:
(1) Replace the "G" board (part # A1054157A) or have it repaired (they repair it on eBay for about $40. You ship them the bad board and they repair it and return it). A new board costs about $80 on eBay without having to send them your (core) bad board. Sometimes they are not available and you must send your board in for repair. this is MUCH less expensive than SEARS, which charges several hundred dollars.
(2) Repair the board yourself- by replacing the two diodes on the "G" Board - (D6301 which is on top- by the small transformer) and (D6116 which is an SMT component on the bottom of the board- it takes VERY steady hands and a good solder iron). The parts should cost less than $25 and are available on eBay by searching for "sony a1054157a".
Location of the "G" board. Unplug the TV set, leave it for 10 hours (to discharge the capacitors). Remove the brown back, carefully unplug the cables, unscrew the two mount screws, and unclip the front retaining tab.
This is the MOST LIKELY failed component, D6301. It is a diode and MUST be unsoldered and replaced. Make sure you know that diodes have a SPECIFIC way they must be installed. Note where the stripe is on the component. You can locate a "good" diode by searching on eBay for "sony a1054157a". You should see a parts kit for about $25, give or take.
One other possible culprit is the D6116 diode. This is a surface mounted component (SMT) and will require a steady hand and a very fine-tipped solder iron. I would replace the D6301 FIRST and re-connect the "G" Board to see if that is the ONLY culprit. If you STILL have the same problem, then replace D6116.