my 42 inch sharp tv has a delay of about 20 minutes before it comes on. that's if you are watching the power light when it comes on if it is red you must press the power button on the remote within a few seconds and the green light comes on. if you miss that red light you will have to wait another 20 minutes.
It looks to me like broken CAP's inside the power source !!! It is charging very slowly.
You'll have to replace the CAP or CAP's which are leaking or are busted (the top is rounded instead of flat or bottom came out).
It is a simple procedure if you know how to solder but it is not simple to get in there !!!
It is dangerous because cap's can keep electricity for long time ! that's why I use Aluminium foil to short circuit the caps and get rid of the remaining charges.
Better to ask someone who knows how to do this.
If you where in Belgium I would do it for a low price ;-)