Cleaning FX-4170 Cooler?

To start with, I'm not entirely sure this is the right section for this question, so my apologies if it's not.
About 6 months ago, I got an AMD FX-4170 for a new computer I was building. It works just fine, but recently when I looked inside to check on the dirt levels, it was absolutely filthy. I would clean it, except for the fact that I can't see any way to get to the dirt. Here's a picture of the heat sink I found on the internet:
http://www.pcper.com/image/view/12389?return=node%2F540...
From what I can tell, it's identical to what I have. It's still been running fine, even though the surface of the heat sink under the fan is covered in thick dirt. The fan almost completely obscures the dirty part, and I can't see any way to get the fan off of the heat sink. There are four holes in the top, but they don't lead to screws - just straight to the heat sink. If anyone could give any suggestions - either on removing the fan, or cleaning the heat sink with it on - it'd be very appreciated.
As a side note, if I remove the heat sink, should I re-apply more thermal paste?

And as another side note, what are some good methods for reducing dirt buildup, aside from water cooling? I suppose frequent vacuuming/keeping away from carpet could help, but is there anything else I could do?

Thanks for the help.