Macbook Pro Early 2011 15 inch, Mountain Lion Booting issue

From the tests you made we can eliminate a list of potential culprit candidates:

1. memory: hardware tests

2. internal disk: use in target mode but you might be tougher on this test: in target disk mode fire Disk Utility and perform some (ex.: 4) Verify disk one after the other.

3. OS: re-install by an Apple service center

Here are the remaining candidates:

1. motherboard
2. graphical cards

Receipe to kill other culprit candidates

If your problem is just due to a graphical chain problem, your system might be correctly booted, but you can't notice it. To check this probability, you will have to set your Mac so as to be able to remotely verify that it is alive or dead.

• Connect the bad Mac to a good one with an Ethernet cable,

• Boot the culprit Mac, even if it does just show you his blue screen,

• Open a Terminal on good Mac, and get the broadcasting IP address. The following command will display it:

      ifconfig en0
  

  behind the keyword broadcast (3rd line). You may also get it at first with a slightly more tricky command:

     ifconfig en0 | sed -n 's,^.*broadcast \(.*\)$,\1,p'
  

  Let's say that it is broacast_IP (most probably it will be 169.254.255.255).

• do a ping broadcast to see how many Mac are alive:

      ping broadcast_IP
  

  if this command reply you with 2 different IP addresses, then you can conclude that bad Mac is alive and its graphical chain is dead.

  On the other hand, if you only get a reply of your good Mac, then bad Mac is really dead, and the last culprit is the good (i.e. motherboard).