Good news. Yesterday I was able to repair my resistor and put everything back together properly. Now I have a fully functioning heat/air setup.
I found an old post with how to fix it by "wadestock" here:
http://www.vehicross.info/forums/showthread.php?t=8099

I decided to go for it. I figured why not, if I couldn't fix it then I would have to buy another one anyways. I used my dremel and cut in to the bottom of the plastic tab that covered the connections. Then I grabbed it with needle nose and snapped it off.
Here is the resistor with the plastic broke off. I grabbed the metal tabs and curled them with my pliers so that they wouldn't try to spring up anymore.



Then I heated up the solder and added a little to it. She's as good as new. If it breaks again, I can fix it.