I have experienced the same exact issue with my Dell Inspiron 15R M5010. I researched the issue and I have found a solution to this problem on YouTube. The problem occurs when the graphics processor (GPU) overheats. When the GPU overheats, the micro-solder connections that secure the GPU to the motherboard begin soften because of the heat, and they eventually become disconnected as gravity forces the solder away from the connections.
1. Disassemble the computer to access the motherboard, and then remove the motherboard from the computer (There is a YouTube video available that walks you through all the steps that I will post at the end of these instructions). These instructions merely serve as a guide to what is involved with the fix. If you feel confident working with electronics, watch the video for more detailed instructions.
2. Use a heat-gun to heat the GPU to about 400 degrees F. for about two minutes. I build model airplanes and use a heat-gun to shrink a film around the wings. I found this works well for heating the GPU. When heating the GPU, focus the heat to only that area of the motherboard. Since you will be heating the motherboard upsidedown, relative to its position when in the laptop, the heat should melt the solder enough to mend the gaps in the connections.
3. Reassemble the laptop and, if you did everything correctly, everything should boot normally.
** To avoid future issues, keep your laptop clean and well ventilated...http://www.youtube.com/watch?v=PJKNGJtk2bo