Weird draining problem - Biting the bullet!

I've decided to bite that proverbial bullet, and just try to fix the !@#$& thing on my own. I think I'm a fairly smart guy, and even though I'm not a professional plumber, I have done jobs similar to this before and completed them without destroying the house. I'm pretty angry that I got so frustrated with this thing, that it just made me more angry that I was willing to give up. So...

The part I'm going to have to get the snake into is that black cast iron drain stack. In order to do that...

Weird draining problem - Biting the bullet!