I have a broken macbook pro with a broken screen

Connect to two Mac via FireWire and the boot the old Mac in Target Disk Mode.

How to use and troubleshoot FireWire target disk mode

The you can use Migration Assistant

OS X: How to migrate data from another Mac using Mountain Lion and earlier

Or just copy the files

You may have to purchase a Thunderbolt to FireWire adapter for the new mac

Or pull out the HDD of broken MacBook Pro and install it into 2.5inch USB external HDD enclosure and connect via USB to get the files on it.

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