So my dad just recently bought a 97 rodeo
today we were wondering why the 4wd light on the dashboard doesnt turn on when the car is in 4wd gears

well..turns out it is a bigger problem than a burnt out dashboard light..

i have the car up on 4 jack stands..and have shifted the car into 4wd..Hi or Lo..and the rear wheels only spin...
Any ideas??

 

i had the same exact problem with mine and last week i put it in neutral shifted into 4wd and then put it back in gear and it turned on just fine, i don't know what happend maybe just messing with the 4wd shifter stick

 

Im thinking it may be something with the vacuum system
the transfer case seems to be ok

 

I know you said yours doesnt come on but the info in THIS POST should help get you started on troubleshooting it.

 

don't know if this helps , i have a 97 rodeo and i had to replace the vaccum actuator just behind the front skid plate. one of them wasn't letting air to flow through to engage the hubs. really easy to replace.