How can I fix my Fuji Finepix S 5700?

Can you switch to the EVF screen? If this too is not working then there is possibly a fault with the display driver. Try using the AV cable supplied with the camera and plug it into your TV. This should work as it's using a different display driver.
If the AV option is not available ( no lead) then to see if the camera will actually take photo's, take the batteries out and leave for a short period. Now load the batteries and switch on. Most Fuji's will have an internal battery for saving date/ time and other settings when not in use. If your camera is a few years old this battery will have exhausted it's life so your camera , when switched on, will ask for date/ time settings to be inputted every time you turn on.
As you cannot see the screen command your camera will not be able to operate until this is either set or bypassed. To bypass the date/time prompt press the display/back button 3 times. Your camera should now be able to take photo's but the date/ time will be factory reset to (I think) 2006-7 but you should be able to use your camera

Dave - Camera repairs
April 2010