What would cause a Drupal site to display a 500 error or a blank page depending on browsers? After moving a site to the final server, I cannot anymore access the site. When I go to the home page, I get a WSD on Firefox, and a 500 error on Google Chrome. 

As it is a shared hosting, I cannot access the Apache error log, and I am wondering if anyone experienced that before. How did you find your way out of it?
The article about The White Screen of Death (Completely Blank Page) is a good place to start.

Depending on your shared host, you can often get access to logs if you poke around your control panel, or they sometimes are copied into your home directory.

Since you explicitly mentioned shared hosting, your best best is to open a trouble ticket.  They can tell you exactly what is wrong fairly easily.

If it is a true 500 error, then my guess is that one of these two lines in the .htaccess is causing the problem.

Options -Indexes
Options +FollowSymLinks


You can try commenting them out one at a time and see what happens.  I suspect that your host has AllowOverride set to None and one of those is trying to set a non-default value that the host has set.