4 wheel drive wont engage 98 blazer, help?

The front axle on my truck isn't locking when I try to put the truck in 4X4. Each switch lights up showing that 4 wheel is engage and can hear a little electric motor and click sound from under the truck I'm guessing from inside the transfer case. Sounds like its locking but the front wheel doesn't seem to be locking. I'm looking for any advice on how to check if the 4 wheel really isn't locking in. And how to check to make sure everything is ok with the transfer case. Any help would be great :)

My 4 wheel drive doesn't seem to be engaging locking the front axle.When I push the buttons they all light up and I can hear like a small electric motor and then a click I'm guessing inside the transfer case, but it doesn't seem to actually be locking or at least didn't feel like it this winter. Any advice on how to check if something actually wrong with 4 wheel and transfer case? And whether or not can be little locking piece in transfer case that commonly breaks and can be replaced?