TV does not turn on model RCA D61W20B

That set uses a color wheel on a high speed motor and a ballast to power the lamp. It is hard to guess at this point what it is without further info.

I would bet the illumination lamp has reached the end of it's life (~$40 online). Should be easy to replace. Also possible the ventilation vents need cleaning, which could cause the lamp to overheat and turn off.

It sounds like it could be your power supply board. You can get one from tristatemodule or shopjimmy. I personally use tristate its always cheaper and Ive had good luck with them but shopjimmy is pretty good too.

Lamp is possible----

Mitsubishi TV troubleshooting
Here's something that might also be useful. After you turn on the set, and get the regular red blinky lights, hold down the Device and Menu buttons together for about 5 seconds.
The Power light will start to flash in a two digit sequence.
For example, 3 flashes, then 7 flashes = 37.
Here are the error codes, and the corresponding problem:
12 = No error detected, check power supply.
32 = Lamp Cover is open.
33 = Air filter cover is open.
34 = Lamp abnormality
36 = Light Engine (DMD or Lamp Fan stopped)
37 = Exhaust or Lamp Ballast Fan stopped
38 = Lamp Temperature High
39 = DMD Temperature High
41 = Short is detected
44 = DVI cable between FMT and Engine disconnected

The set has a 3 strikes and your out (not a joke--what RCA calls this).

It really means a short somewhere, almost anywhere--two things: when you try to turn it on do you hear a faint arc or sound like something sizzles?

Have you done a visual inspection of the main boards looking for anything clearly burnt?

These are not easy sets to work on and frankly I am the only one in our shop who will even attempt to fix one.

What you most likely have is a convergence problem. The convergence circuitry is used to align your colors. What you describe sounds like that circuit has failed. Here’s a link to a decent video that will give you an idea of what is needed to fix it: http://www.youtube.com/watch?v=S6Wa8FvSz-s

the tv won't turn on with the remote or with the power button

same thing mine is doing

it sounds like the power transformer maybe out on the set.it supplies power to the whole set and it sounds like it only getting partial power.

On the Deflection board CK capacitors cp150,cp114 cp120,If cp 150 is puffed up on top it is bad so replace all 3 capacitors 2200uf 16 use 25v and Two left are 220uf 35v Resolder pinns on flyback Transfomer and when re hooking board back up make sure you have second ribbon connector in good. Board next to Deflection is the SSB it has turners on it where you hook cable.