@Sharar, welcome to the forum.
A few things come to mind:
Have you tried things without the new bulbs installed, or with the old bulbs re-installed?
To confirm, the 4wd light is on but the truck doesn't engage 4wd? Have you been able to definitively confirm if it is or isn't in 4wd?
How's your technical aptitude, or willingness to learn? Factory Service Manuals (FSM) are available online, for free, and are an extremely valuable resource. Not talking Haynes/Chilton, but the real Nissan Dealership stuff.
Manuals found here: https://www.nicoclub.com/nissan-service-manuals
Specifically, look at the Transfer chapter (https://www.nicoclub.com/service-manual?fsm=Pathfinder/2003/tf.pdf). Your "All-Mode" system is ATX14A, and there's a self-diagnostic mode described on TS-62. If the dealer inspected the solenoid and it functions fine, you should still confirm if that returns a diagnostic code. Keep in mind many diagnostic codes don't indicate a problem with a specific part, but part of the system pertaining to the part.
The All-Mode system uses numerous inputs. Re-iterating my first question, if you have a known change to the system (bulbs), revert that and re-test. Hopefully it's something trivial, but if it working fine before modifying the switch, then I'd be starting with the switch.