Thanks @hoipolloi for the right direction in finding the solution. Anyway, I had to do a bit different steps to fix the issue.
I my case the UNO had worked fine but suddenly stopped after some playing with sketches. I was receiving the stk500_recv(): programmer is not responding all the time and nothing worked. Then I paid attention that the LED 13 is always ON on my board. It looked like some hard looped sketch was running over and over on the board and was blocking any input to the board. Not sure, it's just my gues.
I tried clicking the RESET at all the possible moments without any luck and suddenly tried the following steps:
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