Sounds very strange as the units are all reassembled and tested prior to dispatch, so should work. Very unlikely that you have a dodgy board or it wouldn't have run in pre-dispatch testing. It's worth checking that the micro SD card is properly clicked into its slot in case it has become dislodged in transit. The unit should show a solid red led on the opposite end of the Raspberry Pi from the USB sockets to show 'power on', then a flashing green as it boots up. It won't go into full operation until it boots up fully and gets a solid gps fix, which can easily take 20 minutes or more first time round and needs a good view of the satellites - i.e. best done outside with a clear view of the southern sky.
PilotAware is extremely unlikely to run off a laptop USB output, by the way. Re your Anker power block, can you post a link or whatever to the model you bought as there have been reports of some of the new versions with 'Intelligent charging circuitry' refusing to recognise the Raspberry Pi. Power Block is still likely to be the best option to power the PAW at this stage.
Regards
Peter