There a re few different scenarios that can be described as the TV not coming on an LCD TV. First consider that a TV has become very sophisticated over the years and needs to boot up. A way of looking at it is the more features the TV offers the longer it takes to come on but I will agree that 10 minutes is excessive. Try to pin point how your TV is reacting to being turned on for clues to what is wrong.
Unplug the TV for a few minutes to let it shutdown and then plug it back in. As soon as you hit the power button listen for a relay click in the power supply. If you hear it multiple times clicking on and off then the power supply it trying to come on, shutting down, then trying again. If this is the case then I would suspect some capacitors to be bad. This could be due to voltage spikes in the supply that are over the rating that the components can handle. This is not definitive but it certainly been the more common cause of this symptom on most LCDs from many manufacturers.
Another symptom could be that the TV turns on, thereâ€™s sound but the picture does not come in for 10 minutes. First check to see if the menu is present, whether there is sound or not. If the menu is there then we know we have the backlight on and that the TV is capable of displaying an image. The source to the TV could be the problem or the compatibility between the two. Try a different connection or a different source altogether. Remember that if it is the TV it will happen on everything. If the TV comes up but there is nothing on the screen, see if you can tell the backlight is coming on. The backlight that illuminates the panel is driven by the power supply. Sometimes the high voltage section is defective but the supplies to the main board are correct and the TV will operate normally but without screen.
The power board or the sources have been mentioned as possible causes but he main board could cause this symptom as well. Since it is where the micro is at and boots up before displaying the picture, any hang up will cause it to sit there. This could be a problem with the board itself or the panel board loading it down. A technician will need to try and isolate the two by unloading it.