You replace it. Not the phone, The LCD screen. It's a HECK of alot cheaper than buying a new phone most of the time. If you go to 'EBAY' and type in the model of your phone, then look for accessories, you may find a replacement screen & PC board...(it's generally a can't buy one without the other kinda deal.) That's how I fixed mine after my niece dropped it. Pretty easy to replace on your own as well. A quick trip to the hardware store will get you the bit drivers you will need. Most of the time they are torx bits & the microbit drivers are about $5 to $20, with replaceable bits.
If the screen is intact try this
I had a phone do this and believe it or not if yours is having the same problem you can put it in the freezer for 5-10 minutes and get about 5 minutes of screen time to recover important messages or contacts. I don't know why but being a computer nerd I figured a deep freeze may help and it did! repeat if necessary.
Also, if that doesn't work for you, then try putting your phone in rice for 1 to 2 days. It worked for me, and my sister