when it is in 4low and you drive it, does it drive like 4low or like 2hi? does it throw a 'check 4wd' light on your instrament panel?
you need 2 things to enguage for your 4wd to work, the front axle and the t-case.
if it is like 4low when you drive around, then it is something with your front axle enguagement... I am having problems with this in my 01 zr2 blazer right now. it can be a bad vacume line, check right on top of the brake master cyl, that line always goes out. if that is good, check if it is holding a vacume at idle. if it is, then take the battery and batt tray out and with jumper cables start the truck and put it in 4wd and see if that vac actuator pulls the cable. it can be a vac switch under the winshield wipers and on top of the distributor in the eng compartment. it can be your cable that goes from the vacume actuator under the battery to the front axle. that is the problem that I have with my blazer, its a PIA to fix.
if you drive it in 4 low and it feels like 2hi then your t-case isnt enguaging and it can be your electronic shift motor, a vacume line, or the switch.
when testing if it goes into 4low, give it some time and go between neutral, D, and reverse while inching back and forth to give it time to fully enguage the t-case.
PS, i think these push button 4WD that GM designed are a huge POS, gives me more problems then it has given me convinience. and it is impossible to convert over to a fully manual 4wd without doing a solid front axle swap.