If it turns on, runs, the shuts off, the temperature is too high, more than likely. Try to keep it cool with a cooling mat, and never sit on a fabric like a blanket or pillow.
Also, you could check you battery settings for when the machine is turn itself off. If your setting say that the machine is supposed to turn off when there is 75% power left, it will turn off when there is still 75% battery left.
Check these things.
Please understand, I have experienced the same problems, practically rebuilt the whole laptop, and it still only boots to run 3 mins or so. Stuff Happens!