Could someone kindly inform me of the location of the auxiliary battery in a 2005 Mercedes-Benz S430 4Matic?

Why was it necessary for me to connect a jumper wire from the 7.5 amp fuse in the passenger side fuse box to the junction box located on the passenger side floor under the carpet to initiate the car's ignition?
 
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The issue may be due to a blown 100-amp fuse, a malfunctioning SAM, or a depleted battery.

However, you do not own a faulty auxiliary battery, since you lack an auxiliary battery altogether.