I shall answer my own question here and hope that it helps someone.
I did the WordPress Automatic Upgrade to 3.0 (and had successfully done it 3 times before). This time I got:
Fatal error: Call to undefined function set_current_screen()in /var/www/mydomain.com/htdocs/wp-admin/admin.php on line 129
Basically the install got stuck at the admin.php file in the wp-admin folder.
Luckily the website was still intact but the WP Admin error was gone.
I followed the instructions from 'esmi' (above) and opted for the 'Upgrade Manually'.
I backed up the site as it was and the MySQL Database (using PHP MyAdmin) - which you really should do before updating your WordPress. Which I didn't!!!
Basically, I then download WordPress 3.0 and removed the wp-content folder (because you don't want to overwrite your Plug-ins or Themes etc). I then logged on to the server using an FTP programme called Fetch (as I use Mac) and:
1. Deleted the folders: wp-admin and wp-includes
2. I uploaded all the WordPress 3.0 files - EXCEPT for wp-content (leave that as it is as it contains important files for your site).
3. Once uploaded I went back to: http://www.mydomain.com/wp-admin. It asked me to Upgrade my Database - which I did. Said it was successful and PHEW.
All was back to normal.
A huge lesson learnt about not backing up the site and database and checking with the host first that it's safe to upgrade.
I was lucky in his case and I hope the above helps at least someone in the future.