My arduino UNO is not responding at all. PLEASE HELP

My arduino is not working. It just glows the "on" LED and the "L"(pin 13)LED all time.
I just tell what happened before this problem step by step:

  1. I uploaded blink example sketch into my arduino
  2. I used a relay board to have the output of the PIN 13
  3. Connected 5V input of the relay to the 5V power pin in arduino. And connected the GND from relay to arduino GND
  4. I used a wall adapter to power my arduino, which voltage is adjustable( I set it to 12v)
    I left it on for 10-15 minutes blinking the light, after some time it was hot.
    then I left it cool down.
    THEN I JUST PLUGGED MY 9V BATTERY TO MY ARDUINO VIN PIN. AND THIS PROPLEM CAME THIS TIME
    "It just glows the "on" LED and the "L"(pin 13)LED all time".
    even i cannot upload a sketch also.
    PLEASE HELP ME TO MAKE THIS ARDUINO TO WORK!
    some information:
    i used arduino uno R3
    i am in india (the country for how is the power supply?)
    adapter bought in singapore


When you say "some time it was hot" what do you mean? What is "it" that was hot? Some part of the board? If so, what part?

The part which is between usb port and power jack.

Those adjustable wall adapters (at least old ones like that - I suspect modern regulated ones exist) are bad news. They usually aren't properly regulated, and under light loads can put out much higher voltage than they're set to.

The second picture appears to show a 9V battery connected to Ground and +5V. That would be enough to fry your Arduino.

A) 7.5V would have been a better choice for your AC adapter. 7V is the minimum and anything higher just produces more heat in the voltage regulator. At 10V only half the power is running the Arduino while the other half is heating the regulator. At 12V it's even worse.