For one: If hosted on a Linux box, why would you download the .zip? There's a tar.gz download available also. That download IS for Linux.
Assume you ftp'd the files up to server (shared host). Did all the files xfer? Did you change permissions/ownerships on the files after uploading? When moving a copy of the config.php file from the old site did permissions get changed on the config.php file?
Since you are remotely hosted, some hosting providers require one to have either php.ini's or .htaccess files to get Moodle to function. Did you have any of those in the old site? Did you copy them over to the new site?
There is one slight requirement change (seen on the downloads page) - 2.4.+ PHP 5.3.2 (min). 2.5 min PHP 5.3.3. Some hosting providers also provide different versions of PHP.
One still might have to take the debug lines from config-dist.php flie and add to config.php file to get anything to show in the install phase.
And apache logs or any other error logs to which you have access showed absolutely nothing?
Hmmmm ... wonder if the install script for the 2.5 requires more memory that your account will allow. Some hosting providers have their systems set such it just kills any script over max ... doesn't log or report anything back to browser.
'spirit of sharing', Ken