So after speaking on the phone with a sizable portion of southern Asia and nearly popping a blood vessel in my head, the situation with HP was resolved.
After being on hold and being bounced around to several different people, I finally got someone. He tried to explain to me that I had a warranty, but my computer was broken, and now I would need to be charged for it.
I finally got a supervisor on the line who took care of the problem for me.
Apparently, they did have my 2 year warranty on file, but I hadn't gone online and activated it. (I guess the $200 charge and confirmation that I wanted the package wasn't enough).
They were using another warranty, which was automatic, but somehow didn't cover my computer. To be fair, Joe did warn me earlier I needed to do that--though I did not remember to do so : /
A couple of things I learned from this debacle:
1.) The word "escalate" can do wonders for your situation. Joe gave me this wonderful tidbit of advice and it worked.
When the customer service rep did not answer me for the 4th time if I had a full coverage warranty (and explained to me for the 3rd time that my warranty didn't cover me because my computer was broken), I demanded that the situation be escalated to a supervisor.
He continued to try to make the same explanation, and I continued to say I wanted the situation escalated. The supervisor got my warranty registered and is getting the refund completed.
2.) Make sure that your warranty is activated. Joe warned me about this one. You figure that the $200 charge, clicking on the YES I WANT THIS OPTION, and the submit payment button would make the warranty happen. It's a stupid step, but it is still a step that would have saved me 3 hours today and had my computer back to me this morning.
Now time to make the rest of my day somewhat productive...and cancel my dream of being on the Clark Howard show.