Try immobilizing the fans with a q-tip or such when it squeaks.  If if stops, you've found the culprit.  Don't do this for more than a second or so.  A new i8200 is $40 from www.parts-people.com   Your heatsink would only make a noise if it sprang a leak, and then it would stop as soon as the gas escaped. 

As I said, even when I disable the fans via software, or when I don't and they aren't running, the noise continues. I completely gutted my laptop to scientifically investigate the source of the sound. It is plainly something attached to the top of my cpu. Fans are not capable of making this sort of noise, especially when they are turned off!

My best guess: http://support.dell.com/support/edocs/systems/ins8200/en/sm_en/battch.htm#1084976

Try attaching an external monitor, then toggle FN + F8 until the lcd is off.  Hear any difference?

When I gutted I had unplugged the lcd from the laptop. I also removed the part you linked me to but not while the laptop was on. I was unsure of the effect it would have on the power switching and did not want to risk frying anything!