to quote from page 18 of the manual
"The camera’s internal clock-calendar is powered by a separate, rechargeable
power source, which is charged as necessary when the main battery is installed
or the camera powered by an AC adapter (available separately). After charging
for about ten hours, this power source can provide roughly ten hours of backup
power. If the main battery has been removed for an extended period, or
removed before charging is complete, a flashing icon may appear in the
monitor, indicating that the clock needs to be reset."
http://www.nikonusa.com/pdf/manuals/.../CP4300man.pdf
So charge it up first!
Presumably its hidden inside so cant be exchanged
edit
You can download the service manual as a 3-part RAR file from
Nikon Coolpix 4300 Service Manual free download,schematics,datasheets,eeprom bins,pcb,repair info for test equipment and electronics That says theres a capacitor in there holding the charge. I assume its soldered to the circuit board - I've not checked the details