Gray screen of death.. need help diagnosing

Hello all, thank you for taking the time to read this.

I have had the grey screen of death for quite some time now. (couple of months)

- The hard drive is fine in target disk mode (ran first aid and disk repair) and I've been able to access data from there.

- I've run advanced apple hardware diagnostics and the only problem that it picked up was a known problem with the airport (wifi only works for a bit when I reconnect the cables and then it no longer works (Wifi not connected error)).

- I can't boot past the gray screen into anything, including safe mode, recovery mode.

- The recovery DVD worked once in the first few weeks of the gray screen but now also only loads to the grey screen. (note: I can hear the optical drive running)

- I've tried to reset the PRAM and SMC multiple times.

- Sometimes the macbook loads up and is stuck on the gray screen and other times it reaches the gray screen and restarts itself.

- I've connected the macbook pro to an external display and saw a similar screen (gray with vertical lines) on the external display.

- I've used the "/sbin/fsck –fy" command in single user mode and seen "the volume appears to be ok".. Anything else I could try?

- I've also booted up in verbose mode. I will attach images of the Verbose mode information at a later stage.

-I opened up the computer and noticed a bit of discoloration in the right hand corner small part of the logic board (see image). There was dust present on other parts of the logic board. Could this be preventing proper logicboard operation.

My questions are therefore:

- Is there anything I could do in single user mode to fix this issue?

- Is there anything else I could try?

- What does verbose mode suggest is the problem? (once images have been added, bare with..)

- If I do need to replace the logic board, is there a point? (I've updated the RAM and it ran more smoothly and I was also going to update to a SSD as well, but given how delicate logic boards seem to be, in buying a logic board, is it worth buying the 2012 version instead? (I was reading on a forum here that you can install a mid 2012 logic board on the early 2011 macbook pro...)

Thank you.