PLEASE HELP: early 2011 mbp freezes, doesn't start up

First of all if you're reading this, thankyou. I've been into the apple store 3 times to no avail, I've shown videos of the problem, many diagnostic tests have been run, but nothing has come up.

Australia, early 2011 15" Macbook Pro, OSX Yosemite (last clean install was mountain lion)

I'll start with what i've ruled out first and then run you all through the problem.

So far I have:

Tried booting aftapping RAM out with known working hardware

Tried booting after swapping HDD with known working hardware

Tried booting in safe mode (hold shift)

Tried booting in recovery mode (hold command r)

Tried booting in verbose and single user mode: fsck -fy to no errors, reboot

And here is what happens (almost) every time I try to boot

(1.)

The initial startup screen (first screen from black) is a shade between green and brown (the colour changes every time)

The apple logo is fuzzy, but the password screen shows, though it too is incredibly 'fuzzy.' (see picture)

>Enter password

(1.1)

progress bar appears (fuzzy, not straight) loads to roughly 1/3rd SAME PLACE EVERY TIME. Then the screen goes black for a second or two and comes back on in the proper grey/white colour but with no logos.

it stays on this screen until shut down using the button, at which point I'll turn it on and go through the same process

At this point I can

Restart without using the physical buttons (press restart on password screen, type reboot in single user mode) in which case:

(2.)

The initial startup screen is white (every time, as if it were starting correctly) however the once the apple logo appears everything is the fuzzy again, the password screen appears (fuzzy), back to square one,

Restart using the button in which case:

See (1.)

Restart in safe mode in which case

Initial startup screen according to method of startup

See (1.1)

Restart (either way) in recovery mode,

(3.)

initial start up screen is according to startup method,

Fuzzy apple logo appears in a fuzzy box, progress bar appears and loads similarly to (1.1)

Restart in Single User mode

Initial startup screen according to startup method,

See 1

enter password, Text scrolls through, hardly legible (very fuzzy)

enter: fsck -fy

Volume was modified message appears

enter: fsck -fy

System OK (not modified)

Enter: reboot

See (1.)

________________________________________________________________________________ _____________________________

On the occasions that the laptop does start up as usual, it is ONLY after pressing the physical button, and I know it will be working straight away as the initial startup screen is grey/white and not the usual /some hue of green/.

When the issue first started, it would turn on and work normailly for a few months before the problem came back (computer freezes, must be turned off with button)

but the more it happened, the more often it happened.

for the last 2 weeks it had lasted a couple of hours of use before freezing again, today, it lasted for a couple of seconds on the first startup, a couple of seconds on the second, and now it doesn't start up AT ALL

My laptop is now a green screen that can be turned on and off with the power button.

PLEASE HELP