Hosting/Domain move - CakePHP modification

I have inherited a website from a business I have just bought. The website was written in the CakePHP engine. I know little about CakePHP. The business is changing names. I have purchased a new domain name, and new hosting. I would like to 'copy' the website from old hosting to new hosting. (Old Hosting is WebCity.com.au. New hosting is DreamHost.) I can provide FTP access to both accounts. I can provide MySQL access to both accounts. I require that the website look and function in exactly the same way just with a changed logo (already sourced) and changed business name including e-mail addresses. I have already identified all pages that need to be edited. (I have tried to simply archive the entire website and upload it to the new hosting, but it doesn't work. No idea what the problem is. Hopefully someone with a bit more CakePHP experience can sort this problem.)