Had a similar problem before on the A340-600.
APU was U/S and so we used on ground power units and an air cart.
We start engine 2 first, then engine 1, pushback, set park brake cross bleed start 3 and 4.
This was the plan, however, we instructed the engineer to give air and opened the start master, when the ground power failed completely after the fuel went in. We lose all displays, bells and whistles going off. I continued the start by holding down the ENG key on the ECAM display and continued the starts on battery, and started engine two as well. Not a big deal, but it could go pear shaped quickly.
There are complications in only starting one engine on an A340 (not all busses are supplied) so you have faults ENG1 EPR mode and other ENG 1 minor faults.
The point is, we had a ground power during the start process and managed to continue on battery by holding down a key for the engine page to monitor and it all turned out OK.