It is seriously doing my nut in,i just want to burn it,only had 6 months and not been far.paid 5k for this and cant drive the thing.Iis there any gear position sensor/switch that may be faulty.It really does need diagnostics, have a look at the LZ map, there may be someone nearby who would come and run diagnostics on it for tea and biscuits.
I'm no expert on the GM box, but it could be an internal fault, the transfer neutral and pinging suggests otherwise though.
Seriously, low battery volts can cause many problems, you need to check the voltage engine off, minimum 12.6 volts, and engine running 14.8 volts or thereabouts.