I've isolated the problem to the battery box. The Smart Inventor V2 board powers on when connected directly to USB. Hopefully it's something simple such as a short in the battery box wire. I'll test it with a multimeter later and report back.
I also have another issue. I'll start a new thread for that, but I can pair the Codrone with the Bluetooth board, but I have been unable to pair the Codrone with an Android Phone and an Android Tablet using the Petrone app. The Codrone LED indicates it is trying to pair, but the "Petrone List" just stays blank. The Codrone shows up as a bluetooth device under Android bluetooth settings, but won't pair there either.