i'm having a very similar problem with my mid 2012 13inch MBP. It was dropped while in the care of a friend about a year ago and was displaying what i believe are called artifacts on the screen immediately afterwards but was otherwise fine, then if you touched a certain part of the case underside the computer would display artifacts, freeze, and reboot after a few seconds. For awhile just checking to make sure the case screws were tight would be enough to boot without issue but it finally stopped booting all together. I didn't see any obvious damage but now the computer will only boot with the top ram slot empty. if i try to insert ram in the top slot (i've tried several cards) it won't boot and beeps three times. could it be something on the logic board was damaged by the shock it sustained? If so what are the likely culprits and how do i go about repairing them? The local mac specialists in my area are just going to want me to replace the logic board which in that case i might as well buy a new one.