Is there a way to access files and information on an offline Linux server

We have a Linux server that was set up with CentOS and cPanel/WHM. It was taken out of service a few years ago but has some files and site information on it that were lost from our current server, and we would like to try and retrieve them from the old one. The machine is a Dell R530 that is just sitting in a closet right now with a display and keyboard connected. Assuming it will boot without an issue, here are my questions: 1) Without killing the machine, is there a way to go about finding and copying the files to an external USB drive, either directly or through another machine, using command line? I know the file hierarchy well enough to locate what we need if I can get in. 2) Can the machine be connected to a router so that I can access WHM using a browser on another machine on the local network? Our office machines are all Mac OS, but I can bring in Windows or Linux machines if it makes for a better solution. Apologies if this sounds like a hare-brained scheme. As should be apparent, I'm definitely not a server technician.