Won't Start and Multiple Electrical Failures

Failure to start could be any of the following:

A  low battery  can cause failure to start as the electronics require at least 10 volts to work properly.

However if turning the ignition key produces no action at all then
  1. the  battery condition  is important on all modern cars. Ensure the battery is up to scratch; they can fail suddenly.
  2. the  brake light switch  may be at fault as it is part of the ignition circuit on automatics - it is up underneath the passenger (RHD cars) glove-box
  3. some have also found that the  starter motor  fails when hot but can be OK after it has cooled down.
  4. an  automatic gear  fault can lead to a failure to start as the two ECU's (gearbox and engine) talk to each other.
  5. if the  ignition key  has been damaged or opened up for any reason then make sure the transponder is still present
  6. The Security Module can get upset if the battery is dabbed on/off; doors repeatedly opened by hand (as opposed to normal electrical operation) - in which case try a  battery reset 
  7. Dead car after battery has run flat.

The car may have entered "economy mode" if for example, you were cleaning it with the doors open and radio on and run the battery down to trigger the warning. Normally this isn't a problem and the car starts normally, but apparently Peugeots can occasionally be a pig to get back out of this mode.

The trick is to run a thick wire from the battery positive terminal directly to the starter motor and force the car to turn over with the ignition turned on. This makes the car start and come out of Economy Mode.

Once started leave the car running for half hour or so to let the battery charge up and for everything to reset itself.

 further information on the BSI and possible repairs 

Multiple Simultaneous Failures