That sounds very much like a failed electrolytic capacitor in the power supply board. It's easy to spot; the top of the capacitor is bulged up and may be leaking material. Usually, there is more than one bad capacitor. See the attached photo - two of the three capacitors shown are bad.
To get replacements, you need the following information: Capacitance, printed on the capacitor label (e. g., 2200 uF where the u is actually the Greek letter mu and stands for micro-; this would mean 2200 microFarads),
Maximum Voltage, printed on the capacitor. The replacement may have a higher voltage rating, but not lower.
Maximum temperature, printed on the capacitor. The replacement may have a higher temperature rating, but not lower.
Diameter of the capacitor in millimeters. The replacement may have a smaller diameter, but smaller diameter capacitors may not meet ripple current or endurance specs (described later). There may not be enough space on the board at that location for larger diameters.
Length of capacitor in millimeters. If it is too long, you won't be able to fit the cover back on without damaging something.
Endurance: at least 6000 hours at maximum temperature. For 10 mm diameter capacitors or larger, you should be able to find 10,000 hour parts.
Ripple current: You want the maximum ripple current rating available consistent with the other specs, otherwise the new capacitor may burn out prematurely. Higher voltage capacitors often have a greater ripple current rating, and physically larger capacitors likewise.
I have had excellent result with Panasonic FR series capacitors. They are much better than the Chinese off-brands usually installed in LCD TVs. When you install the replacement capacitor, make sure the polarity band goes in the same way as the original (the board is probably marked to show which way), and use lead-free electronic solder with an iron that gets hot enough for it. There are static-sensitive parts on the power supply board. Do not touch the circuit conductors with your fingers; handle the board by the edges only. Do not place the board with the wiring side down on any surface except an antistatic mat.