I'm 23. Weak back muscles causes pain in entire back, shoulder n neck. High fatigue. Caused by wrong posture while using laptop. How can I strengthen?

Tai chi. Besides strengthening your lower back muscles it is imperative to strengthen your upper back and neck, abdomen, hip flexors, and buttocks. In addition increasing your flexibility is key. Tai chi exercises have shown in several studies to statistically decrease back pain so join a class.
Back workout. Take Naproxen (aleve) twice a day and rest until your pain is gone. Then try the balanced circuit training exercises shown here: http://youtu.Be/godiqsneusu.