I had written Frederick about this through his support function within his great plugin. I thought I would also bring it to the attention of people that might encounter a similar error.
I recently switched hosting from TCH over to Mediatemple. With any WordPress migration, you generally export your database and import into the new installation.
I got my WordPress websites running simply by copying over the old files to the new server and edited the WP-config.php to locate the new database.
I then installed fresh copies of W3 Total Cache on these sites.
I came across an error looking for the old path locations at public_html. The new server doesn't use such a path. Hence, it sends out a "fatal error" and asks for you to set permissions under the content folder to 777. Of course, that still doesn't work because the path doesn't exist.
According to Frederick, this is not an issue with W3TC at all, but rather it has to do with the database. I agree with him.
However, that still doesn't solve my issue. I was wondering if anyone experienced something similar, and if so, if you managed to fix the database so that W3TC installs to the proper directories.
Once again, I think we all need to thank Frederick for this great plugin. He's really overdone himself here!