I read it. I'll take that cookie now.
But seriously, it's not too tough to take apart a classic Xbox. The big problem is that they're heavy and bulky, but like any other tech product, they can be disassembled if you know what you're doing. That's where iFixit comes in... look at this guide and it'll take you through the steps of disassembly.
https://www.ifixit.com/Teardown/Xbox+Teardown/1324
You'll need to flip it over, remove the rubber feet on the bottom of the unit, and take out the screws hiding beneath them. I think there's also a screw hiding under a sticker. After all the screws are taken out you should be able to flip it back over and pull off the top of the case. You'll have to take out the hard drive, DVD-ROM drive, etc. to reach the motherboard, but that's only if you want a really thorough cleaning.
Also, 1.6 model Xboxes don't really need to be hard-modded. A soft mod is generally good enough... just make sure you've got all the necessary parts before you begin. If you make a mistake you're going to want to have a copy of Halo 2 or some other recent Xbox title handy to reinstall the dashboard... otherwise things can get really unpleasant.