Take the HDD out and start up the machine. Let it go to the flashing folder and you are now confirming it stays on. The folder will stay flashing as long as you leave it telling you there is no OS X present. At least now you know it´s not the logic board. On Mac Book Pros if the hard Drive is failing it will constantly shut down. Take the drive out and test it with Hard Disk Sentinel. More than likely it will be in the red. Just put a new HDD and you´re golden. Don´t fuck with the RAM. Don´t bother resetting VRAM PRAM.