Hi CarynG,
Here's something you can do to test your WordPress setup on this problematic site:
1) Create a file, called z.php (actually anything ending in .php) and put it in the root folder of your WordPress install. Contents of file:
<?php
require('wp-load.php');
$x = mkdir(WP_CONTENT_DIR.'/upgrade/');
var_dump($x);
$y = mkdir(WP_CONTENT_DIR.'/upgrade/testing');
var_dump($y);
?>
2) Then visit that file in your browser, i.e. go to (having changed the URL to match your site):
3) Then please tell me what the output is!
If it shows errors and/or says "false", then you've got a file permissions problem. If not, then the problem is elsewhere.
David