Changing host problem

i am currently in the process of taking over control of the website for my buiseness, i will be re hosting the site my self on a new site (probably hostgator) but i do not have acess to the current controll pannel to make a back up of the files so that i can re upload them on my new hosting account

is there a way to change over the host whilst keeping the website live, and not having to have the database backed up and uploaded to the new host ?