Recently my Xbox 360 doesn't want to display anything on my TV and the green light turns...

If the console has the red light and not the power supply then this indicates the console has suffered a hardware failure, Do you not receive any on screen error code before it shuts down?

Which model of xbox 360 do you have? If it was set down a little hard have you checked to make sure the hard drive is fully connected to the console as this can produce the red light issue.

Usually though if theres no on screen display when the light turns red then this means either the gpu or the video ouput has failed, Unfortunately if thats the case its not really fixable yourself (an E74 error code with a gpu failure can be in most cases
repaired with the heatgun trick, I have done that one to a few old 360 consoles and been suceessful)

It's also worth checking your video cable from the console to the tv.

The symptoms you have shown though would in most cases indicate that your gpu as failed on the console which was very common especially on the 2 older 360 models, the original and the elite.

Flashing orange, solid red, or no light: Your power supply may need to be replaced. Try the following solutions:

1. Plug your console’s power supply into a different electrical outlet. Do not use a surge protector.
   
2. If the power supply light is solid red or flashing orange, unplug the power supply and let it cool for 30 minutes. Then, plug the power supply back into the outlet.
   

If your power supply light is still flashing orange, solid red, or unlit, your power supply needs to be replaced. You can
order a replacement Xbox 360 power supply from our Xbox Online Service Center. Console registration is required to replace the power supply under warranty (the power supply
warranty is the same as your console warranty).

when i turn on my xbox, the lights are green on the ring as normal like it should be but screen on the tv is still black. on the power brick the light is green

I have a similar issue, when im done playing, i turn off the tv and the xbox and the green light flashes, not fast but softly i should say, and the fan is still on but it doesent show anything on my tv screen help plz

The noise it makes is less than one second, you try to turn it on, but the green light doesnt appear, or anything in the screen, the sound comes from the xbox it self, not the TV.