4wd sounds healthy, but doesn't work...
 

I have a 1998 blazer 2dr auto.

My 4x4 is not working. The push button switch always lights up correctly in all 3 drive modes. I can hear the transfer case click when in the vehicle, and I hear a "slurp-click" type sound coming from under the truck (which I assume is good)

However, doing burnouts on an icy street has revealed that the front wheels do not spin, in either 4hi or 4lo, which is puzzling given that all seems to be in order.

Any ideas? I tried searching but couldn't find anything that fit my description accurately...

Thanks!

sounds like a vac leak
have you checked the actuator under the battery tray ?
look if the hose is connected to the vac resi . It looks like a huge ball under the hood

read this over it might help also

4x4 No Worky.... Maybe this will help.... - Blazer Forum - Chevy Blazer Forums

No I haven't checked it. I will tomorrow. What should I look for as far as good/bad indicators?

Check and see if there are any tears in the rubber around the outside of the actuator. Also, make sure that you don't have any unattached vac lines under the hood near the actuator and vac accumulator (big black ball either attached to the hood, or in the drivers side fender.)