You are doing well, Robert.
1) I still wonder what version of Moodle you were running. Moodle 3.5 requires php 7. Here's how to check. In cPanel, File Manager, navigate to your Moodle folder. There is a file named version.php. In it, near the bottom there should be a line as follows:
$release = '3.5.2+ (Build: 20181027)'; // Human-friendly version name
1) What does yours say?
2) Do you know if you had additional plugins installed? Beyond the normal?
3) See if you can succeed in installing the PC installer version of Moodle. It is Moodle 3.5.3. Just do the basic install. Don't worry about anything else, just see if you can get this running on your PC. The only tricky part is if you are running Skype on your PC because Skype uses the same "port" as Moodle. If this is your case, then you need to explore how to disable Skype or more its port. Help is on Google search. What I am trying to do here is to get you to a point where you can restore your moodle into your PC local version of Moodle. But one step at a time. Two paths, however, I am moving you to install everything on your PC, and at the same time continuing getting you to this VPS issue going.
4) It is odd that you could compress your moodledata folder, but not your moodle folder. Typically, moodledata has many more files (I think.) But not a big problem since the moodle folder normally contains only moodle. However, while you are at it, see if you can download config.php which is in your moodle, to your PC. This is an important file to have. Keep it with your backups of your database and moodledata folders.
VPS discussion ...
Many server providers use that AMP stack. For example, from GoDaddy, I have a Linux server, the ability to install either MySQL or MariaDB, and I can install a variety of php's. So it is similar, but more powerful (VPS) than the PC install of Moodle. With a VPS, you usually have some very good flexibility. In my case, GoDaddy expects you to know what you are doing.
On a VPS, a moodle install is actually pretty simple. You download and uncompress moodle into a "web" folder, such as public_html or htdoc. You create a database, use utf8mb4.unicode_ci, give yourself full rights. Then you create a moodledata folder, one level down from public_html. Then in your browser you go to htttp://yourdomainname.com/moodle. Moodle will start its install. So there is only three things, the database, the moodledata folder, and moodle. If you make a mistake, no problem. Delete the database, delete the moodledata folder, delete the moodle folder, try again. And again. And again. This is how you learn. Also, if you get your PC version of Moodle running, which is an AMP stack, the steps are nearly identical. You can install more than one moodle, practicing while you go along.
So, is LunarPages offering you a VPS? Or are they saying "You install on your own?" Where are you with LunarPages?
No, nothing is that scary. A VPS (from GoDaddy) comes with many features installed. This is the beauty of a VPS. I don't have to do a lot to get mail working, for example. On my GoDaddy VPS (and from many companies), yep, I get cPanel. You are familiar with cPanel. And File Manager. Have you explored creating a database? cPanel normally offers a tool to do this. But a VPS does have just a few tricky things that need to be done, making it a little more mysterious and troublesome.
To find the version of php that you are really running, put the file below (info.php) into your web folder, then do a www.yourdomanin.com/info.php and you will see your php version, and a bunch of other things about your php.
Yes, 2GB RAM on a VPS is the minimum. When I was buying a new VPS at the beginning of this year, I experimented on a GoDaddy 2GB VPS. It worked fine. But then I bought a 4GB VPS just to have some extra room.
Okay, enough for now. I will let you continue. You are making some good progress.
Pay attention to what Ken tells you too. Ken and Usman are really good at help folks. I am at a much lower level.