Use the camera to look at a photo that you previously took.
If that photo displays OK, then the LCD screen is OK.
If not OK, suspect the LCD screen itself.
Next, reset the camera to the factory settings:
Look in the User Manual for a Troubleshooting section and you will find an "Initialize" command.
Go to the page indicated and Initialize the camera.
This resets the camera to factory specifications.
If that does not fix the problem, suspect the CCD sensor.
That is the device that turns light into an image.
Take a photo with the camera and view it on the LCD screen (if you can).
If it appears to have captured an image (any image), copy the image to your computer.
View the image with your computer.
If the Image looks like your example or similar, the CCD sensor is bad.
Now you have enough information and it is time to call Sony Repair and ask about repair costs.
I have had my Sony DSC-T77 for around 2 1/2 years now and all has been fine...then I switched it on the other day and the screen looked like this:
Any idea what component has fried and what I need to replace/fix to get it fuctioning again ok. (Would it be as simple as a new screen/digitiser only?)