Normally a router should reissue the same ip address if available, however rebooting it will cause it to forget the DHCP pool and potentially a device with a valid unexpired lease could be using a different IP from what the router thinks.
I would expect that rebooting the router should cut the power on the network cable for about 30 secs and the HDR-1000S should see this and try for a new ip when the power is restored. The LED on the network socket shows the presence of power or not.