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[COLOR="Blue"]And I could here the sound of clicking and buzzing sound as usual.[/COLOR]
I am not sure what you mean by the above.
Th compressor should not be doing a lot of clicking as this is a symptom of it trying to start. For some reason it cannot and then the overheat trips and it retries once the compressor cools down.

First thing you want to check is if the compressor is running all the time except when the unit goes thru a defrost cycle. You can usually hear it but also should be able to feel it vibrating.

It should be on all the time as your freezer temperature is high so it should be trying to cool it down.

If it is on all the time, is the evaporator/freezer fan also on?

If both are on, remove the rear cover in the freezer and check the evaporator coils.

If they are iced/frosted over to the point that the fan cannot pull air through them you have a defrost problem.

If there is just frost in one area (usually where the freon enters the coils) then it is probably a sealed system problem. This will be an expensive repair as you need a pro.

[COLOR="Blue"]--> No, it doesn't run all the time. yes I could hear it and also feel it. Once it clicks, buzzing is following and it goes for a while. But it stops. And when compressor is running, evaporator fan runs as well. I think here is the suspicious point. Even thought the temperature is high, the compressor is not running all the time.[/COLOR]
Yes the compressor should be on all the time except when in a defrost cycle.
The above points to a bad main control thermostat as the unit is cycling but is shutting off too soon.
You could check this by unplugging the unit and shorting the two wires at the control thermostat together. Just be sure they cannot short to anything else. Then plug it in and monitor the freezer temperature If it gets down to 0 to 5 degrees F then you know that the unit is capable of doing this and it is just a control problem.
Do not leave the thermostat shorted. This is just for testing.
If it does not get down to the temperature and cycles then it is probably a sealed system problem. The compressor is overheating and it's thermal protect is opening killing power to it. Then when the compressor cools the protect resets and the compressor restarts.

[COLOR="Blue"]--> I removed all the ice from the coils but it is not alive.[/COLOR]
Not sure what you mean by "alive"
If the coils were heavily iced/frosted over re : a defrost problem, and you manually defrost the unit then it should work OK for at least a couple days until the ice/frost builds up again impeding air flow.

[COLOR="Blue"]--> The frost was over half of the entire coils, does it seem okay?[/COLOR]
Should be a fairly even coating over the entire coil surface but sometimes it depends when you checked it.
Below is a link, check out the example pictures about half way down the page.
http://www.applianceaid.com/ref...ator-not-cold-enough.php