So, I tried what I did in my earlier post.  Please, do not do this at home and if you do, I will not take any responsibilities if anything goes wrong.  Anyway, I opened up the receptacle for my range then I went to my electrical panel to turn on the breaker.  With my girlfriend's hair dryer in one hand and its plug in the other, I carefully touched the ends to the hot wire on the right and ground/neutral.  With the right hot wire, I was able to turn on the hair dryer and get it to work.

However, when I try to do the same thing to the hot wire on the left, no go.  This has been my trouble all this time!  Essentially, I think what happened was that some moisture got into the flooring while I was gone (due to the house being so cold and all) and corroded the aluminum splicing of this wire.  It seems that someone has done this before and they didn't rewire, but that they just spliced the connection.  My plan right now is to run a new wire to replace this one, but I'll probably get one that is rated to be outside.

Since I don't want to take apart all the insulation and tear up the belly wrap to my mobile home, I will just run the new wire underneath my home.  As suggested by a few people, I should get some sort of SER wire…who knows what that is, but I will soon :).  Hopefully, when I am done with this, I will be able to cook again!