Is your site connected to cloudfare, or similar service? Is your woocommerce database hosted on the same server as your website or is it get the product info and such from another server somewhere else?
You can try clearing all caches again, then deactivating the plugin, followed by a uninstall of w3tc. Before you reinstall delete the w3tc-config folder on your server if its still there as if its left all of your same settings will come back one your reinstall w3tc and the php script for w3tc in that folder may still be somehow affecting your .htaccess file even though the plugin is disabled. I would then turn on each feature, especially the minify features, one-by-one and check Woo functionality.