Hello!
Usually, when a camera lens/shutter does not open, it's usually because their is some grit or grime that has gotten into the shutter (You might hear a grinding noise when the camera comes on and get a lens error). Cleaning the area with alcohol might help.
There is also the chance of the motors that open the shutter may be failing, which are difficult to replace.
As a last ditch effort, you could attempt to replace the battery, since old batteries might not be giving enough power to actually open the shutter even if the rest of it manages to power on.