This sounds like a very common issue.
If set is hard to turn on (takes several tries)but will eventually turn on here is what my guess would be.
Every set has a standby power supply
that is running 7/24 if the set is plugged in and it supplies voltage to the remote circuit that turn on the main power supply for the tv and hence turn the set on.
This is an area where companies cut corners by using lower rated voltage caps. By this I mean Standby usually provides under 10 volts to trigger the set on----what they do is use filter caps rated at say 10 volts max in a circuit with 9 volts (example)=with the standby on all the time the filter caps (electrolytic caps) dry out and fail.
The problem usually begins where you have to turn set on or or two times and gradually gets worse--takes longer and more tries to get it to come up.
Once on it will stay on until turned off for a period of time.
The caps will begin
to work better (regain some of the capacitance) as they get hot--hence one it is on it will seem ok.
of this problem is most of them happen when set is a year or two old (no warranty) and all you have to do is look at the top to locate bad ones.
They are generally black or blue and round and vary in --they have two connections each--a + for positive and a - for negative--not unlike a battery
which in a way they are. The + and - are marked on top and bottom of most boards.
They are easy to replace and not expensive parts.
The tops are silver
and metal looking with creases on top and if bad they will be puffed up on top---tops must be perfectly flat with no brown material leaking top or bottom.
If this is your problem once you id them (make a drawing) you can begin.
Here is the critical part---on each cap is also marked the value like 220uf 10 vdc---220 micro farad at 10 volts maximum.
If you find for example 6 puffed up and all are 10 vdc replace them with the same value capacitance (like the 220 uf) but go up to at least in this case (from 10 volts) to a 16 or higher rated voltage cap.
The only issue is when you go up in voltage rated value the cap is larger so sometimes there is an issue of physical space for the replacement on the board to fit them in.
The reason they cheapen these sets in this way is if 10 caps and you make 25,000 sets there is a considerable savings in parts cost.
They do not care as long as it lasts past the usual one year parts warranty.
I have taken the time to be long winded because this really sounds like it may be the problem you have.
See attached photo of a typical cap and if you have questions or need advice let me know.