Well, just after posting this, I finally managed to fix this problem. Here is how I did it if anyone else runs into this issue.
1. Run regedit
2. Go to "HKEY_CURRENT_USER\Software\Microsoft\Windows\Shell\Bags\1\Desktop"
3. Locate the "LogicalViewMode" and "Mode" keys
4. Bring up the Windows...
I appear to have some how placed my icons on my desktop in Tile View. I cannot for the life of me figure out how to restore the icons to their normal appearance. Any help is greatly appreciated.
Here is a printscreen of a portion of my desktop so you can see what I'm talking about: