The soul is not immortal but ceases to exist the moment the body carrying it stops functioning. There's a reason the words soul and life were used interchangeably in the Greek New Testament. Your soul is your consciousness, without the brain and biological processes carrying your soul it is nothing, just like a broken computer can't run any programs. If you doubt the brain/soul connection just look at people who suffered brain damage and how much their souls changed as a result, they are completely different people.