kmessinger on "Admin White Screen, Admin Slow, Admin Posts and Pages Disappeared Gone"

This will give you some insights in speeding up the site.
http://developers.google.com/speed/pagespeed/insights/?url=http%3A%2F%2Ffranklinfitnesscenter.com%2Fcms%2F

If I reinstall WordPress, will it effect my database?

No, not if you do it the correct way.
https://codex.wordpress.org/Installing_WordPress#Detailed_Instructions

Where does my database live?

It lives on the web server provided by your host.

I've made backups of both the site and database. Can I apply them to a new installation of WordPress?

You can use them but reinstalling is easier.