As long as it's a gray screen your Backlight and inverters are working
Black screen just after it dies....I would say the inverters aren't energizing the lamps/backlights.
If it shuts down and you power it right back up....and it stays ON for a real long time, then I'd say it's not a backlight inverter issue.
But the 6 Blinks is telling us the backlight is bad.
There's only one thing that might lie to us.....the Micro having low voltage.
A micro running at 3.5 volts instead of 5 volts could trigger false failures and also shut down too.
I would expect other symptoms....TV not responding to remote, picture scrambling, menu or volume or channel changing by itself.
the screen turns a grey then in a few seconds the picture comes in clear
That statement right there makes me think we have system control issues. Your TV should turn on, glow gray, then come on within 2 seconds.....IF it takes 5 or 10., then that's really SLUGGISH in my opinion !
And for some reason....in the back of my head somewhere....something is telling me to replace the Main board, because I've seen that before.
The turning off...the sluggish picture....something keeps telling me it's the main board.
Does my description of the TV's behavior seem to match what you've been seeing?
If you turn it on....does it stay on sometimes and it seems to take a long time for the picture to appear?
That right there is something I KNOW I've had to deal with before.