Hello and welcome to Tom's Hardware Forums.
First, what's the make and model? Changing the screen isn't the rocket science most people think - in fact it's quite easy and most laptops are worth the trouble.
Second - when the external monitor goes off, pull the cable from the laptop and then reconnect - it may show the picture properly.
The main thing is your files are safe in there. You could if you decided not to repair this machine, take the hard disk out and buy a USB converter to be able to access the files through another computer.