Hi @jameslk2131 ,
Try taking a picture and download it to a computer and check if the picture is OK or if there is just a black image or even if you can access the camera OK. I realize that you cannot “see” what you’re taking in the camera’s LCD screen but this is just to test if the problem is with the LCD screen only or with the camera’s motherboard.
If you can take a picture and can download it and it is OK then the problem may be with the LCD screen. Initially as a DIY repair all you can then do is to replace the LCD screen and check if it works OK.
I cannot find a Finepix S4300 LCD screen replacement guide or teardown video, but here’s the ifixit [guide|51629] guide that may help as hopefully the cameras are similar.
I couldn’t find a replacement LCD screen part online for your model, (or even for a S4200), you may have better luck.
What I did find however is [https://www.ebay.com/itm/Fujifilm-FinePix-S4200-14MP-24x-Optical-Zoom-FOR-PARTS-ONLY/143669480910?epid=1622819882&hash=item21735e4dce:g:hQsAAOSw-btfIy68|this]. Everything that I could find indicates that the same LCD screen is used in both cameras, so this can be used as a donor parts camera. Given the cost it may be an option to consider if you also cannot find a screen.