moving old wp install to a new server

Hello Support!! I need help moving an old wp site to a new server. A new site is in the works, but in the meantime I need to get this old one moved. It's an old version of wp. When I update to the current version of wp it breaks the template. So, in trying to move it over directly without updating, I'm having issues with the links not working. Messages about mysql_connect being deprecated as well. I can see the index page and the login page, but when I log in to admin I get a blank page. Links to existing pages are also not found. What are the basic steps that I'm (obviously!) missing to get wp onto this new server? I've got cpanel access, updated database location/credentials in config. Halp!! And thank you in advance!!! -B