waddell68 . Remove the battery and memory card from the camera, clean your battery contacts with ink eraser on a pen/ clean cloth/Qtip and then blow out any dust/debri. Install new good quality batteries in ((correct orientation)) and try powering up camera. If camera does not turn on, problem could be with internal switch connection or the main circuit board bad. You could disassemble the camera clean all the connections and secure them. If not comfortable opening camera have a good camera shop have a look, diagnose and estimate repair. Find below a link to your cameras manual, check through their trouble shooting section,etc.. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
http://www.fujifilm.com/support/digital_cameras/manuals/pdf/index/j/finepix_j100_j120_j110w_j150w_manual_01.pdf