Display showing whiteout (or colored fuzz) then shutting down

My macbook pro started having this problem about 4 months ago. When I'm working on it, the entire screen suddenly displays colored fuzz (like the black and white fuzz on an old tv screen when there's no signal, except it's also colored). Then after about 30 seconds of doing this the screen goes black and the computer shuts down.

I've tried connecting it to an external monitor by HDMI but the external monitor shows no signal when the laptop does this. I took it to an apple store about 4 months ago (when the problem started) and they said it could be something with the graphics card. They wanted to charge me $400 to replace it. Unfortunately I wasn't in a position to do that.

Another thing, I use my computer for movie editing and am in the middle of a huge project. So the laptop has been getting a lot of graphics work.

Last thing, I have traveled lots with this computer including the dusty outback in Australia. Could this problem be because of dust on the logic board? Or has anyone else had this problem?

I really appreciate anyone's help.

Hunter

Ok, so so far it seems to be running okay. It still seems a little slower than usual but it hasn't shut off.

Here's what I did: As per Dan's suggestion I removed the logic board and cleaned all the dust off of the board. I didn't reapply thermal paste.

There were clumps of fuzz clogging up the vents to the fan and the top side of the logic board was covered in dust. After taking it apart I used some canned air to blow it off and then some q-tips with isopropyl to clean it further. Then I reassembled everything. Here's some pictures of the parts with dust and then after cleaning:

I'm using the laptop right now to do this post and I have final cut pro running in the background and so far it hasn't shut off. I'm hoping and praying this worked!

If I continue having problems I'll let you know.

Thank you all for your suggestions!