If you are seeing the home page, you're connected to the DB, so that's not it (unless someone has left an index.html file in the root with an old static copy of the home page).
The first thing to try is manually deleting the files in the core/cache directory.
Second, did you copy the backup files in using FTP? It's fairly common for files to get corrupted or missed when you're transferring that many. It's better to .zip them up, transfer the .zip file, and un-zip them on the server (see the upgrade link below).
Since you found the core/config/config.inc.php file, you're definitely using MODX Revolution, but who knows which version.
Normally, I'd suggest re-running Setup, but you'd need to upload the correct version of the setup folder and we don't know what exact version you're running.
In the unlikely event that the setup directory existed in your backup and is there, try:
yoursite.com/setup
Don't proceed unless the "Upgrade" box is checked.
If none of that works, I don't usually recommend upgrading a broken site, but in your case it might make sense. There are some steps to do it here:
http://bobsguides.com/modx-upgrade-faq.html
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PLEASE, PLEASE specify the version of MODX you are using . . . PLEASE!
MODX info for everyone:
http://bobsguides.com/modx.html