Chris was quite helpful to get me on the right path. I have outlined the steps below for us QNAP users:
Step #1: Download WinSCP (or if you're further advanced feel free to use ssh).
Step #2: Log-in to the NAS as admin
Using username "admin".
Step #3: Change directories to wordpress
[~] # cd /share/Qweb/wordpress/
Step #4: Change the file permissions of the current folder and sub-folder contents
[/share/Qweb/wordpress] # chown -R httpdusr:administrators ./Step #5: Exit the console
[/share/Qweb/wordpress] # exit
Step #6: Open your browser, get back to your WordPress admin console
Step #7: Pour yourself a nice beverage
Step #8: Enjoy!
As soon as you're done, make sure to start updating everything.
Security tip: Outdated WordPress installations and plugins are bad.