ping does have a broadcast option on Linux you may try.
Look somewhere on the camera for a MAC address, which, if it's Ethernet, should be somewhere on the device, or possibly in the device's set up menus if it has any. You can then arping to see if it obtained or tells you what it thinks is its IP. If you can get into the DHCP tables of your router or DHCP server you might check there for any hostname that suggests a camera, if it grabbed an IP address.
Otherwise, if you believe transmission is taking place, you'll need to fire up a packet analyzer and snoop on the interface it is connected to. tcpdump may help, as well as Wireshark or its command line equivalent tshark may be useful.