Unable to boot MacBook Pro in Yosemite, garbled graphics

Hello,

I'm hoping someone can help me as I'm tearing my hair out here.

My MacBook Pro (late 2011) has been having problems the last couple of weeks, to say the least. I think they are all connected to Yosemite 10.10.2.

The major issue is that 99% of the time it is not able to finish booting. The progress gets about halfway there, then the screen goes white, the fans gradually increase in speed to a really high speed, then the system restarts. In addition, from the start of boot up there are jagged horizontal red lines all across the monitor which disappear when the screen goes white.

What I've tried

• I have tried starting in Safe mode, but the same thing happens.
• I cannot start in Recovery mode by pressing Cmd + R - the computer loads as if I've not pressed any buttons, then follows the same process as above.
• I have an external hard drive with a Time Machine backup: I have tried loading from this (by pressing Option after the chime) but again the same thing.
• I have used the Hardware Testing tool but no faults were found.
• I can start in Single User mode and have run disk repair.

The baffling thing is that every once in a while, the machine will boot and run absolutely normally. However if the computer sleeps, it will not wake up properly (it hangs then restarts, then back to square one).

Last time I did manage to boot up, I ran disk utility (no problems found) and checked the console log. This was filled with Kernel errors: unfortunately I didn't make a note and now can't access the console as I can't get in to the system.

As an example, the machine hung waking from sleep 2 and a half hours ago and I've still yet to boot it back up successfully.

Does anybody have an idea of what action I can take to get the computer to boot? I am thinking this is something with Yosemite 10.10.2 as the problem has only started since downloading the latest update.