From the service manual:
Fuse # 4
Amps:15 A
Component(s) or Circuit(s) Protected
Ambient light, Audio unit, Audio remote switch light, Dash lights brightness controller light, Cargo area light switch light, Console box light 2, Cruise contro lmain switch light, Front side marker lights, Glove box light, Hazard warning switch light, HVAC control unit light/Climate control unit light, Interior light switch light, License plate light,Moonroof switch light, Navigation display unit, Navigation unit, Power mirror switch light, Relay control module, Seat heater switch lights, Select/reset switch light, Taillights, VSA OFF switch light, VTM-4 switch light
Fuse # 5
Amps: 20 A
Component(s) or Circuit(s) Protected
Audio unit
Fuse # 32
Amps: 7.5A
Component(s) or Circuit(s) Protected
Accessory power socket relays, Audio unit, Front accessory power socket relay, Gauge control module,Ignition key switch, MICU, Navigation display unit, Navigation unit
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Sounds like you are using factory head? If thats the case you likely found color code info on the forum? Also sounds like when you connected power to a battery source, both acc & batt lines to head unit were connected together. The hiss you are hearing is the amp remaining on, which *might make sense* now that you have ign and batt + to the HU connected to a battery source, as seen by the clock remaining on. With the amp trigger wire connected to the batt power line feeding the HU, the amp is idling full time, drawing current from the batt. Is there a reason both acc & batt lines are connected together? If not, connect both HU acc & amp trigger wires to "acc" power in the factory harness. That way amp will only power up with key on and clock will turn on/off with the key.
But that doesn't solve the problem of the batt line being dead in the factory harness. Hopefully, the fuse info above will be helpful. The root of power loss was the circuit got overloaded most likely by the power amp. My guess is the fuse is popped, you just haven't found it yet.
Edit: fuse info above came from 06 thru 08 service manual. Based on your description, it *appears* fuse 32 popped. That is, IF 06 thru 08 fuse assignments remain the same to 2012. End edit.
Best of luck.