I hate to say this but I think you know enough about computing to be dangerous. I think you have been too ambitious, and not taken into account how Moodle works.
Whenever you want to install Moodle on top of an existing Moodle site you need to rename your OLD site to MOODLE_OLD before you do anything, that way you are then safe to add your new Moodle install.
When you set this new install to work, you can be sure you are not using ANY of the old files, (which in your case are corrupt), and so when prompted you just tell your new Moodle where to find the database and where to find Moodledata. A better way would be to create a new database, then you would be doubly sure you have a fresh start and NO corrupt data too.
From what I can gather (especially seeing that you have some OLD files in there) it looks like you overlaid an older version of Moodle on a newer version....(for example: Moodle 2.0.7 on top of Moodle 2.2.1) probably becasue I alerted you to the fact you probably had the wrong version in the first place. So now your problem, although partially fixed is still pretty much messed up.
If I were you I would cut my losses, delete the database, and delete Moodle and begin again.
This is a hard way to learn about Moodle, but better in the long run.
Also...and this is perhaps more important. PLEASE make sure you choose the correct version of Moodle for your host site. Find out what version of PHP is running on HostGater. Each version of Moodle has a specific minimum requirement. Check that out first before you download it.
Hope this helps?