Some suggestions:
1) If your laptop has an external display connector, just connect it to a monitor with an appropriate cable.
2) Get it repaired.
3) If you are handy with these things, remove the HDD from the laptop and connect it directly to a motherboard port, then copy what you need from it.
4) If you are not handy, have a friend who is handy do it, or take it to the local PC shop and pay them to do it.