I fixed it! Haha! It runs, it heats, nothing has caught on fire or blown up yet. A successful repair day.
The UPS man was kind enough to drop off my parts early this morning, and I spent several hours stringing these spring like things (I think a real repair man would cry to hear the heating coils referred to as 'spring like things') through the back of the dryer. Thanks to a very nice man with a foreign accent that was thoughtful enough to put explicit instructions on the Internet, I got it all back together. I had a few left over screws, but I'm not overly concerned about them.
The kids, while all this was going on, ran amuck. They watched way too much TV and feed themselves cold macaroni and cookies for lunch. They looked at me strange when I expressed my enthusiasm over how the dryer turned and warmed clothes at the same time.
I am ridiculously proud of myself. I feel like I've just preformed a successful heart surgery or something. I was trying to remember if I was this excited when I got my Master's Degree... it's too close to call.
The only problem is now I have an unhealthy attachment to this appliance and will probably never be able to get rid of it when I finally kicks the bucket.