I have a 2001 4x4 blazer and it wont go into 4wd. When i push the button to go into 4wd i can hear the transfer case shift but it seems like the front wheels wont engage. The light will just blink. I and put it in 2wd high and 2wheel drive low. Some times when i turn it seems like the right front cv axle will bind up and you can hear it pop and it will go into 4wd. I think it started one day when i was pulling out and old ranger we had in our yard. I was trying to pull it out of a hole in reverse and it would spin the tires then make a sound like i was striping the cv axle. It would only do it after about spinning for about 2 seconds. Every time it makes a noise it seem to come from the front right wheel area. It late and i can really think staight so if you need me to test anything or have any questions please ask. I can get to my favorite fishing hole without 4wd. I runs fine in 2wd.
Thanks

 

I had the same problem on my 99 but it would never go into 4 hi or lo. After doeing some test there was a vacuum switch that was out and after about 80 bucks it works fine now. Dont know if this is your problem since it did go into 4hi but could check it out

 

i had that problem in the winter time. although vacume problems always occour with these things with lines drying up and cracking up. i think your problem might be the trans axle. if it does engage slightly and you apply some power and it trys but doesnt seem like it locks in all the way and makes grindy cruch noises . but if it does nothing at all wont even go in likely vacume lines. or the vacume acuator under the battery