Ializ you are amazing! I am truly grateful for all your help and input!
I did what you said, I made sure that all the urls in the wp-config.php were correct, and this time it worked!
For my site it didn't like the /wp/ suffix after the URL, so I tried it without and it's working now.
The only thing left to do was remove and re-add all my media files, and go through the site editing all of the links as they were out of date and still using the previous url - A small price to pay methinks! Phew! Wine time.