Kovid, thanks for your reply.
I tried setting the Calibre software up as a server per the instructions in the manual that you linked me to and still no go. I'm pretty much giving up at this point thinking that I can connect my tablet to the Calibre software.
Not only does the Kindle software not have the ability to browse with an internet browser (when you click on the Kindle Store link it takes you directly to the Kindle store and there is no way to enter your own URL), but when I attempted to connect to port 8080 with the standard internet browser I was unable to connect. This may be an issue that has nothing to do with Calibre, but I'm at my wits end.
I've settled for connecting my tablet as a USB device, copying the .mobi files that I created in Calibre over to the external SD card on the tablet and then having to disconnect from the PC and manually copy those same files into the the folder used by the Kindle software. I'll post back and at least let everyone know if the Kindle app will then recognize my books.