As mentioned above, even though the old MacBook display is broken, you may still be able to connect an external display and have a functioning computer.
Here is something else to think about:
Assuming your old MacBook has a hard drive that is "readily accessible" (easy to take out), take it out and put it into either a USB3 enclosure or a USB3/SATA "dock".
You can find instructions on how to open the MacBook and remove the drive at ifixit.com.
You'll need the right tools (the guide will tell you what's necessary, probably a small screwdriver and a small Torx-type driver -- you can pick these up cheap at stores that sell tools).
This is not difficult, anyone can do it (even an old ham-handed guy like me!)...
Put the drive into the enclosure or dock, and attach it to the NEW MacBook, and it should "mount right up" on the desktop. You can then get what you need from it.
After you have the new MacBook configured as you wish, you could even re-initialize the old (now enclosed) drive, and use it as a backup...