Start by checking the "Possible Causes" listed above. Visually inspect the related wiring harness and connectors. Check for damaged components and look for broken, bent, pushed out, or corroded connector's pins.
There is a Factory Service Bulletin for the 2004 Infiniti G35:
2004 Infiniti G35 Factory Service Bulletin OBDII Code P1051
The bulletin suggests reprogramming the Engine Control Module (ECM) first before replacing any parts.
The cost to diagnose the P1051 2004 Infiniti G35 code is 1.0 hour of labor. The auto repair's diagnosis time and labor rates vary by location, vehicle's make and model, and even your engine type. Most auto repair shops charge between $75 and $150 per hour.
The current amperage in the heated air fuel ratio (A/F) sensor 1 heater circuit is out of the normal range. An excessively low voltage signal is sent to Engine Control Module (ECM) through the heated air fuel ratio (A/F) sensor 1 heater.
The Engine Control Module (ECM) performs ON/OFF duty control of the Air Fuel Ratio (A/F) sensor 1 heater corresponding to the engine operating condition to keep the temperature of A/F sensor 1 element at the specified range.
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