How to move a WordPress website with same domain to a different host?

I am moving a website to a new host (to GoDaddy) for someone (same domain different host), I was sent the old files: one database file and a folder with all the WordPress files named “site”.

1. I created and uploaded the database – In the database I saw the wordpress address was set to website.com/site and the site url was website.com.
2. I changed the wp-config file, I kept the same database name/user but changed the host to “localhost”
3. I FTP’d all of the website files to the server. I put index.php in the root and kept all other files in the “site” folder. Also in the root I created a .htaccess file with:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
Etc.
4. changed DNS

After this the website just showed blank pages. The only way I could get it to work was I uploaded all of the files to the root directory. If the files are in BOTH the root and the “site” folder the website works fine. I tried changing the General Settings WordPress address to the root and that also didn’t work. And one other strange thing, I can log in and edit the pages (it uses VISUAL COMPOSER) but in the WordPress Dashboard “Plugins” is not there. Any ideas what I am doing wrong?