Engine will not start

I got RAC to look at the car and he diagnosed fuel pump, checked the fuel pump, all OK. Checked the fuel pump relay, diagnosed it was sticky, jump started with directed cable connection to the positive bolt in the engine, the car started. Left the car running for about 15 minutes then drove for about 500 metres, TRANS FAIL-SAFE PROG message came and the car limped and cut off all power. Disconnected the batteries to reset, but there was no power still. Called out RAC again, he checked the batteries and both brand new batteries were down to 0. He concluded there was serious electrical problem. The car had to be flat bed recovered to the garage. The batteries were disconnected while we ait for the recovery vehicle for about 30 minutes, then reconnected the batteries so I can roll up the windows, there was power and the engine started. Attempted to drive to safe location off the main road, 50 metres, the same message came on again. Any ideas?

Thanks Dr Hagerty. Update above.