Possible water damage to logic board from June how to fix?

Hi I have a 2011 MacBook Pro 17 inch. There was a spill in June I opened it and dried it did not see any liquid ... But forgot to look at the sides where it might run off the keyboard..

Now here in august it chimes and then goes into a reboot loop. We ruled out the hdd at the apple store and they saw the liquid indicator was on. So they are saying it's the logic board.

Any help with fixing this or knowledge of what may be going on and how to fix

Thank you !

Here are pictures of the logic board.. The only area I'm questioning is the lower rt back above the ram

If the damage is the lower rear right .. Can I clean it and fix it some how? Thank you!

Here are pictures after the alcohol and toothbrush ... Does it look better?

Any other things I should look at or do before I put it back together?

Also someone mentioned the gpu would that be a factor?

Nick, do you see the corrosion? I have removed the logic board ...

And do you think the alc and tooth brush will remove the corrosion and let it work again?

The dust on the logic board.... The toothbrush and alc? Is there a particular area I should not use the tooth brush on?

Is 91% ok

Here are pictures of after the alc and toothbrush.. Am I missing anything.? Does it look better?

I hate to ask .. Just making sure I am not missing anything

Thank you again for your help

Someone mentioned the gpu what are your thoughts?

Ok.. Here you go

I have done pram, smc I put in the maverick install on a stick and it recognizes it when I choose it instead of the bootable hdd (did disc utility 3x pre problem and when we looked at the hdd at the apple store through another mac) all good!

it goes to boot into it (apple / cog wheel) then gray screen

Same with doing internet recovery

I do not have the os disc but like mentioned above .. It tries then gray screen