Try unplugging it for 10 minutes and then plugging it back in. I had this problem a few years ago with a Toshiba. The power supply was bad. Usually in instances when it won't turn on but lights blink, it's either the psu or something inside is faulty.
This is by no means a cure all, but a solution that I've had luck with in the past. (Disclaimer: Doing this risks permanently damaging a board, I only use this as a last resort if I'm going to replace a board anyway).
On two different TVs I've fixed them by baking the faulty board in my oven @ 350F for 15 min.
The heat "reflows" the solder connections and can potebtially revive dead boards.
The first TV was a LG 42LK550. Had problems with the main board, TV would work for 5 min and shut off. Baked the board and it worked fine ( I used it another 6 months and sold it) .
The second was a Sharp LC-32D62U no picture no sound with a OPC/Power, Power, Power blink code. Testing pointed to a bad main board. Baked the board and TV is going strong again.
Each time I removed the boards, and disassembled them as much as possible, removing as much rubber and plastic as possible while leaving the board intact. I then placed them on a cookie sheet and baked them.
Again I ONLY use it in situations where I would replace the board anyway. But at that point what have you got to loose.