Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
Sounds like a basic start up issue. If the TV eventually turns on and displays a picture, but it now seems to take "forever" for it to light up and display picture and sound, then it most likely is a computer and "heat related" issue.
The computer isn't recognizing OK signals from the TV screen stating the screen lit up/energized ok.
That's what I initially suspect in your situation.
So the key....let's unplug the TV's power cord to clear any bad software running and get it to reload first.
If your TV is older than 2009...you can unplug it for 10 minutes. If its 2009 and newer, you need to unplug it for 20 minutes since the Energy Star ratings changed in 2009.
That will reset the TV's software
After that, Try to darken the room so you can see if the TV screen stays pitch black or it glows.
The TV must glow before the "computer" recognizes it is glowing and the switches on the picture and the sound.
That's usually the reason you're still seeing the green light flashing.
Check it out, let me know the results.
While you're back there unplugging the TV set, get the TV's model number also. There's a sticker on the back with the giant main model number, but the "Product Service number" gives more information.