Drupal - Drupal navigation always returns a 404 error

Option 1 - RewriteRule and RewriteBase

Check if you can use an URL containing ?q=user or ?q=admin. Refer to my answer to the question "7.26 /admin, /user not found on Localhost" (which is about RewriteRule) for more details on that.

In that answer there is a link to the question about "drupal /?q=user is working but /user not working", for which the accepted answer of that question provides more details about tuning RewriteBase in your .htaccess.

Option 2 - Admin option 'Clean URLs'

I you can use the ?q=adminURL, then try to navigate to /index.php?q=admin/config/search/clean-urls to check the current status of clean urls (if it is enabled or disabled). Make sure "clean urls" is enabled.

Refer to "Clean URL leads to duplicate URL after migration to another hosting" for more details on that.

Option 3 - base_url

Make sure the value of "base_url" is set correctly (in your settings.php).

Option 4 - .htaccess file

Verify if the .htaccess file is present in the directory where Drupal resides (and/or that it is not incomplete or corrupt). If it is missing, then upload it. If needed copy it again from the "Drupal" archive file (.zip or .tar) from Drupal.org again, and just use that new .htaccess file.

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Note (about your "The ?q=admin URL didn't ask me to log in" comment to this answer) Check if you get the same problem using another browser. If with another browser it works, then that part might be a cookie problem (delete the cookie in the browser where you have the problem, and try again).