Toshiba Satellite M35x-S1142 Turn off problem

Question

My laptop has a slightly different shutdown problem than the others I've read. It starts to boot up, the "Windows starting" blue screen/message appears and even sometimes my Windows wallpaper appears. Then suddenly, the laptop turns off. Instantly. I've suspected a power issue but I can boot into SAFE boot mode and the laptop works fine. This leads me to believe its not a power problem. What about a memory problem? I've reloaded the HD using the restore disk and I have the same issue. Doesn't appear to be a heating issue. Battery charges fine and I have the same results with or without battery or AC power.