You never told us that you were using DB Cache. This had nothing to do with W3 Total Cache.
Now one look at DB Cache's compatability section should have told you not to install this plugin (0.6) because it is only good up to WordPress version 1.27. Also, the installation instructions to DBCache spoke of db.php which would have clued you in.
To look more into the problem, I tested this on a clean install with current version of WordPress 3.2.1 and DB Cache 0.6. What I found was this:
A) After enabling the cache, db.php shows up in the wp-content folder. db-module.php (part of DB Cache) gets copied as db.php. db-module is an copy of the core file wp-db.php. All are of the same version (0.71).
B) After ticking the enable cache checkbox, I proceeded to get errors everywhere I attempted to navigate within the WordPress dashboard. Namely, this error prevented use of admin and at this point was hosed:
"Fatal error: Cannot redeclare class wpdb in C:\wamp\www\iwordpress.com\wp-content\db.php on line 54"
This problem is being caused due to a conflict in the naming of the database driver class. In require_wp_db(), wp-db.php is loaded and if db.php exists, db.php is loaded as well. But because both files declare a wpdb class, this error occurs. Developer needs to create a different class name and rewrite code to fix this bug.