I would suggest using ncftp if you are going to do this over FTP.
It's very easy to use and install (lenny: apt-get install ncftp)
You could then connect to the server where your website currently resides and just download it onto your new server.
Just make sure that you use ncftp on your new ISPConfig machine and that you are logged in as the user for the correct new website on that machine or you might end up in having permission issues.
Another possibility would be, you take a windoze machine, install a free ftp client like filezilla, download your website from the current server and upload it to the new ISPConfig machine.
Hope this is somewhat clear for you and helps you out !