Well turns out it didn't like the backslash at the end. I had this:
shadowspawn D:\\Laptop\\ Q: Robocopy Q:\\ "N:\\My Computer\\backup\\Laptop\\" /E /LOG:N:\\BackupLog.txt
It didn't work, so on a hunch I removed the backslash at the end of "Laptop" to this:
shadowspawn D:\\Laptop\\ Q: Robocopy Q:\\ "N:\\My Computer\\backup\\Laptop" /E /LOG:N:\\BackupLog.txt
This worked flawlessly now, so just another thing for everyone to look for.
Now that I've finally gotten this to work (first +rep for you guys helping), I wanted to mention a couple of initial observations. First, this tool is very helpful if you want to back up files from multiple folders on your computer without having to remember which folder to look for to back up each time you do it. For instance, if you want to back up your music folder in My Documents, but also the folder where your Outlook database is stored, and everything on your desktop, it's an easy way to do it each time since it remembers all the locations for you.
Second seems to be my only beef about this so far. It appears that this backup method doesn't take any less time for the actual back up time. I tested with a small folder to compare. The folder and contents were 334kb and took about a second to copy with the traditional copy and paste. With robocopy, I timed it to be about 13 seconds. I'm starting to wonder if this will be problematic when I start looking at my work files with multiple folders where each folder is several GB's of info. The amount of time for it to complete a back up with large folders may be more than I can handle.