Clearing the cache breaks the installation I just moved my Drupal 7 installation to another server. All the domain names are exactly the same. Everything seems to work fine until I click on clear caches. That results in a HTTP 500 error which I am unable to debug since the host does not display the errors.

I have sql dump for my db that is right before I hit the clear caches so whenever I fully restore the db in that state the site is back up again. That tells me that it is a database issues but I cannot figure out what it may be.

Any ideas?
You need to check the PhP error logs on your server for the reason for the 500 error.

A quick guess would be that your backup excluded the actual cache table structure and not just it's contents.  So when the code needs to access one or more of the tables, it is not there.  The log should show you the specific problem.

An alternative would be to use something like MySQL Workbench and working / non-working databases and start comparing tables between the two.  Missing tables should be fairly obvious.