Phone finds Network only when cable is plugged in

Having received a phone with unknown history and having reset/ updated everything the phone did not find a network, despite no sim problems and Imei and Modem settings clearly displayed ( no IC chip fault).

1)

By there luck I noticed that, once connected to USB cable ( cable not yet plugged into computer or charger) the display lights up - that should. not be ?.

2)

With cable inserted and connected to MacBook ( and wifi on f that matters) the Phone now immediately logs into the mobile network of its simcard ( not using this provider in other phones so I am sure this is not a shared connection).

Unplugging the cable from the phone immediately has it searching for signal again, not finding any until I plug it in again.

I am a bit lost on this, is that a hardware or software fault ?