When transferring large amounts of files I use one of these.
Just unplug the data cable from the computers hard drive, plug this in and power up the computer. (it won't boot, we just want the hard drive powered up)
Then plug the USB end into the laptop and the computer's hard drive shows up in the laptop as another drive.
Then just copy and paste anything you want to move.
I also use it to recover stuff from a non bootable system, as it gives direct access to the drive with another computer or laptop even though there is no functional operating system.
SATA/PATA/IDE 2.5 3.0 to USB 2.0 Cable Serial ATA Adapter For HDD/SSD Hard Drive 5075684375947 | eBay