Hi,
Based on your description the caused of this symptoms was the
faulty electrolytic capacitor in the power supply board. Leaky/dried filter electrolytic capacitor will
dropped the supply voltage and will disable the unit. At the first stage of the symptoms,
warm up will make itself stable but it will get worst, times will come that the unit will not even power up.
Leaky electrolytic capacitor has a physical indication of fault like
bulged/dome at the top and can be easily identify. See sample picture below.
Dried capacitor has no physical indication of fault, you must have a
capacitor checker to determine its condition. If not available you must replaced all of them in the power supply board with same capacitance and voltage rating which is printed in its body itself.
Another option is, you may replaced the entire power supply board, click this
link for replacement.
If you don't have necessary tools and test instrument and can't troubleshoot the unit yourself, I would advice you to look for a qualified tv technician to isolate the faulty capacitor.
Hope I helped you.
Have a nice day!
Thanks for using Fixya.