Bad caps...you got bad caps, no matter HOW FLAT and Perfect they look.
Yes, they will bulge and crown as time passes by...
James knew, but the caps haven't visually died yet, and you don't have an ESR meter, and I wouldn't expect you to buy one unless you were a TECH...
Bench Tech that is....not a field Tech.
They're kinda salty....
Ok, let's COMPARE the cost of buying a power supply ---VERSUS--- the cost of the caps, solder, solder wick, SOLDERING IRON , and your time .....
Personally, I 'd just get the board and not worry about testing and finding them -- that's for guys with Lab Coats like this character --
Yeah, I'm thinking of changing my Avatar -- This one character epitomizes how the rest of the world sees most techs...made me laugh the moment I saw this 20 years ago.
I'm just going to do the research now....
Model number -- LN40A500T1FXZA
Hmm, no service bulletins about the bad caps on your model...there is one about the TV shutting down, but that's not your symptom.
Your's won't start...
But the LVDS cable should be unplugged on both ends to "buff" the contacts, it can cause a startup problem, AND if you disconnect ONE END and it starts reliably, then I'd replace it.
LVDS part number -- BN96-07161C
Don't buy one, just disconnect it and see if the TV turns on and off reliably.
This place has pictures of a lot of the boards, no picture of the LVDS cable, but it's a GOOD REFERENCE so you can use it to verify what board we are talking about.
Now the power board's part number is *****BN44-00199A
And that's only $50 for the board, cheaper than the cost of a soldering iron, solder, caps, wick etc...and easier for you to install.
Here is where you can order it --
ShopJimmy has the better price than any other.
Run that LVDS cable test, and if it starts when cold, plug it back in and see if it fails -- that helps to VERIFY the problem as the LVDS cable, or the power supply board !
If you have any questions, just ask