There's some trickery about the fog lights that you need to keep in mind. Your headlamp switch needs to be in the ON or AUTO position before the fogs can even be turned on, if that's not the problem then you should check the fog lamp relay in the IPDM (fuse box with a cover on it behind the battery), you need to pop out the ***-snaps that hold down the plastic cover over the battery compartment, you can't just access it through the little battery window opening.

Check fuse 72 (15amp), fuse 73 (15amp), fuse 80 (10amp), and the fog lamp relay. Check out the FSM under section PG page 24 here.

http://www.nicoclub.com/service-manu.../Sedan/2003/pg

Basically how the system works, power is initially fuse protected on the control and signaling circuit, signal circuit goes to the SWITCH which then goes to the BCM. Control circuit goes to the RELAY and when the BCM gets the signal from the switch it closes the relay which powers the fog lamps. Canadian models have a DRL module that makes the system twice as complicated...

I would start by checking the fuses, if they work then turn the headlights ON, verify they are on, have a second person turn the fog lamp switch on and off while you sit at the IPDM with your finger on the fog relay and see if you feel the relay click, if not then replace the relay. If it still doesn't work then either the combination switch (fog lamp switch) or the BCM or wiring between those components is messed up which are lengthy repairs.

 

Keyless system ALSO failing is a bit of a problem since it too is controlled by the BCM, now you have two unrelated BCM systems that are failing... if you can't get the fog lamp working then it would probably be worth a trip to Nissan for a diagnostic of the BCM to ensure it's still working properly because it's one of those items that can quickly leave you stranded on the side of the highway if other critical systems give up the ghost.

Do all the steps of the key fob programming work properly except for the final step where you press the button on the fob to actuate the locks? Make sure you are performing STEP 6, that's when it finalizes the fobs!

https://www.autotalk.com/infiniti-g3...ructions-2178/

 

 

Take it down and get the battery load bank tested, it's probably just old and dead and in need of replacement. Old dead battery can also cause all those issues.

EDIT: Get your diagnostic done at Nissan, they're half the going rate and competitive with nearly every other mechanic shop.