There is a technical bulletin on Topix - 'LTB00540v4 - Engine Will Not Crank/'Smart Key Not Found' Message Displayed' for Discovery 4, Model Year 2010 Onwards, VIN: AA513326 Onwards, where the Keyless Vehicle Module is either replaced or software upgraded, but the symptoms are mainly related to the message centre display 'Smart Key Not Found, Engine fails to crank and vehicle may not lock/unlock'.
It might pay to have a dealer check for this issue - 'Lock up of keyless vehicle module (KVM) - LTB00540v4', but with the other signs of no indicators showing on the dash and no A/C - heater, I would be guessing a short or bad earth connection.
If when you moved the loom in and around the battery case it all came good, you may possibly be in the right location.

