I have no idea what to tell you to try next. I've never attempted any sort of camera repair. Have you tried finding a manual to see if there are any trouble-shooting directions? Link to manual:
http://resources.kodak.com/support/pdf/en/manuals/urg00740/ZD710_UG_GLB_en.pdf
Below are the two things to try if the camera will not turn on (source: user manual):
1) Insert a new or charged battery.
2) If practical, connect the camera to a Kodak 3-volt AC adapter
(sold separately), then try again. See page 62 for more battery
information.