Electronic 4x4 shift?

I have a 1997 Yukon with 225000KMS.     I bought the truck with the 4x4 not working and i am trying to diagnose the problem so i can buy the right parts for it and take the right course of action.

It has the electronic shift on the buttons on the dash (2HI 4HI 4LO)

when i push the  4x4 button, the light for 4 hi blinks but never stays solid, and the front wheels do not engage at all.  If i put the truck into "4LO" the transfer case puts the gearing to "low range", however the light constantly blinks and the front wheels do not engage.  

I know there are 2 actuators, one for the transfer case and one for the front axel or diff or something.  I am wondering if it might be one of these 2 actators, or if it could be something in the transfer case, or what?

If anyone heere has had any experience with this, please let me know what you think and what i should check for.  when the vehicle is in 2wd should the front drive shaft turn? I haven't checked whether or not it does but i am thinking of checking that.

Any assistance (that isn't a form of advertising for any auto parts website) is greatly appreciated