I'll add to this, since I just diagnosed this issue recently and couldn't find anything about it here on the forum.
Symptoms were the same, no 4WD light when the push-button 4wd was pressed (with 4wd also physically not engaging).
While looking through the wiring diagrams, I noticed that...
I sent a PM, but I'm not sure if it went through... Interested in the cylinder heads off of your 96 engine. Please shoot me an email at [email protected] if you didn't get my PM. Thanks!