Why won't my Samsung LCD TV LE40B651T3W turn on?

On the first day that it started acting up, it randomly turned off and immediately back on again, but this was the first time and I thought nothing of it. The next day it starting happening more frequently and the following day even more until on that same day it turned off and was completely dead. There was no red standby light. A while later it automatically turned on again and acted up like before but this time it completely died when it turned off. Now it's gotten to the point where it's off with a red standby mode light, the TV won't respond to any buttons. If I try to turn on the TV using the power button from the Sky remote AND the TV remote, it won't respond - the red light won't even blink. It won't even respond when pressing the touchscreen power button on the TV either. From this point it just randomly turns on, stays on for 10 minutes or so then either turns off and on or turns completely off, with no red light. I've opened the back and checked the insides; I'm no mechanic, but everything seemed fine to be. The capacitors seemed normal, no fuses were blown, it looked like everything was in perfect condition. However, there was quite a bit of dust around some of the electrical parts and everywhere in general - could this be a cause? I'll try cleaning it anyway just to check. Please help.