Likely what is happening is the PSU is detecting that the battery is low and automatically shutting off the computer to protect the battery, and enable you to still start the car.
Lead-acid batteries only give off gas when they're charging, not when they're being used. So when you charge the battery (presumably you'd do this with a wall charger), leave the boot lid open and open the compartment to the spare tire, and this should provide adequate ventilation. You may want to place an exhaust fan there as well just to be sure.
Hope this helps.