After one year of trying to solve problem why I cannot login in EE administration when I use session variables I have found an answer.
Session variables were encrypted by web hosting company and that was main problem for session variables not working. since I had same problem on other server also, other hosting company, I mentioned that to them, they stopped encryption and it started to work.
I am mentioning this because I had this problems for very long time, and there were threads about that but no answer other than to change to cookies mode.