Damn Plumbing

I have run into my first home problem. I pride myself in the fact that I can generally fix anything that I run into...granted it may take me a few hours and I might cause irreversible damage in the process.
However, this morning I have been completely bested. My kitchen sink keeps backing up. I first saw it the first night I moved in, but after getting it cleared I haven't had a problem since.
Last night, I cooked for my brother and sister. It was a great dinner, but then the problems started. This one was so bad that it was backing up into the dishwasher and everything.

After doing some research last night and dumping 3 containers of liquid plumber into the drain, I got up this morning and when to Home Depot. I brought home a manual crank auger (snake), a pipe wrench, and a bottle of clog remover that was so potent that the plastic bottle was sealed inside a plastic bag...Surely, I had this clog bested.

I dismantled the p-trap and got all 25 ft of the snake in apparently without hitting a clog. Damn...maybe I loosened it up. Re-assemble the pipes, pour in the clog remover, and let sit.

For the next hour, I was confident and had kicked the clogs butt. Unfortunately, I failed.

But my tenacity didn't allow me to admit defeat, so I went at it again...3 hours later, the clog was still holding firm.

But I have a lifeline....home buyer's warrenty....I put in my call to HMS.
"How can I help you today?"
"Yeah, my kitchen sink is clogged and I need a plumber."
"Ok, we can do that, but plumbing work that is the result of a stoppage or clog is not covered."
"What?"
"Yes, it's right in your coverage agreement."
...ruffle through papers...
"Dammit"
"We can still send one out to you."
"No thanks. I'll handle it."

Next call...Richfield Plumbers..."Sorry, our hours are M-F 8:30am to 7pm"
"Dammit"
2 more plumber calls failed.

Finally, I resorted to Roto-Rooters.
"Yes, we can help."
"How much?"
"Free estimate and then they can start work right away."
"Score. Send them."

I saw this as a huge victory. Everyone told me that plumbers cost anywhere from $75 - $100 just to show up at your door. I got mine for free.

An hour later, the plumber was here.
"Your drains clogged?"
"Obviously."
"Ok, I can clean it out for $185."
...Head Drops...
"Dammit. Ok, let me get my checkbook."

And here we go. He's been at it for about 15 minutes now. Sounds like he's finishing up. Hopefully this will have solved the problem.

Chalk one up to the previous homeowners...They got me good on this one :(