Hi,
Try taking a picture and downloading it to a computer to check if the picture is OK. I realize that you cannot”see” what you are taking.
If the picture is just a black image then you have a problem with the camera’s motherboard or CCD image sensor or both.
If you get a “good” picture then most likely the LCD display is faulty and needs to be replaced.
Here’s a link to the ifixit [guide|24724] guide which may be of some help.
Replacement display screens are available online. Just search for ''Canon PowerShot SX120IS LCD screen part'' to get results for suppliers of the part.