Connect laptops with non working monitor

Hello,

my old laptop monitor stopped working and it's always black, so while I can start regularly windows I cannot see anything. I am about to buy a new laptop and I was wondering if there's a way of connecting the two laptops since I'd like to transfer all the files on my old hard drive into the new machine. I read about lan usb or ethernet cables, but what exactly can be done in my case since one monitor is black?
thanks a lot! David