I've had a couple instances where I restart the computer and the display is black (no cursor) but the computer is on. The keyboard illuminated and beeps when I hit return indicating a failed login attempt I believe. If I put the computer to sleep by closing the lid, opening the lid results in a successful startup from sleep with the usual login screen. External display (HDMI or Thunderbolt) are not recognized. I've reset SMC and PRAM which have not helped. I disconnected the internal battery connection which someone recommended. This fixed the problem for the next startup but it has returned. Obviously, I don't want to continue to open the case to keep things running. I noticed Apple had an extended display issue repair program that my computer was eligible for, but it expired in December 2012. Is this a logic board failure? Any thoughts greatly appreciated. Thanks.