I’ve had some problems with installing WordPress to sub-directory, as I found out later – ‘cos my inattention.
First you have to check General Settings > WordPress address (URL) & General Settings > Blog address (URL), then set Permalinks and upload next .htaccess file to sub-directory where WordPress located:
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /blog/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /blog/index.php [L]
</IfModule>