@Tim ... ahhhh, one of those 'one click wonder' installs.
Question about is it permissions ... don't think any change to an admin setting would also change ownerships/permissions to folders and files in code.
In admin of a Moodle, please understand that the moodle interface as an admin level isn't the same as admin of a site using cPanel. And that sometimes, especially with an issue like this one, you need to locate things like web server (your site runs nginx) logs and be able to view them to see what they might say. Can do that with cPanel, I think.
'One click wonder' installed the data directory in code folder ... which is not recommended ... but since it worked at one time ... and now doesn't, leave it where it is. Normally, if an admin did that, an .htaccess file would be placed in the moodledata directory to help protect it. nginx (your web service) doesn't use .htaccess files so ???? (one click wonder!)
What I suggested to you was to remove the trailing slash in your config.php file for the path to your moodledata.
This part ... 'when I checked a couple of the login boxes on the admin settings in moodle site admin' ... someone would have to be able to do a Vulcan Mind Meld to know exactly. Do you recall what those settings were?
This is where looking at nginx access logs might provide the url to your site which would give us a clue ... otherwise ... guesses.
Note: your provider saying there was a missing index.html file code code root would really indicated, that person has not a clue ... moodle code as well as any web server app that used php would have index.php default files ... not index.html.
At this stage ... you might have to re-install ... did you have any courses developed or being used?
Think I'd try this first:
Go directly to this url ... you change 'site' below to your URL:
https://site/report/configlog/index.php
That's a form that shows all the config changes to a moodle ... since it does require a login, you will be prompted to login - if you can - it will then forward to that report.
'SoS', Ken