I have changed my J1 status to F1 in 2009. Since than I am studying here, in USA.
Due to political and economical crisis in our country, my parents can not support me for a long time. The situation became more serious after the local war in the region where I am from.
I have read that after first year in F1 student status, I am allowed to apply for employment authorization on Form I538 based on financial needs arising after receiving student status.

What is the possibility of getting the work authorization in my case?

Thank you for your answers.

It will depend on the country conditions and how well you can document the changed conditions. You must discuss with your DSO/FSA, as they are allowed to approve work authorization, usually on-campus employment. Remember, that even with the EAD, you must still maintain a full course load, unless otherwise approved by the DSO/FSA.