4x4 Transfer Case ( NO axel lock in)
 

I have a 1995 with a floor shift. With the emergency brake on. I have the engine running and the transfer case in 4lo. I put it in drive and the front end jacks up like it is in gear. The floor shift does not light up indicating that the front axel is locked in.
I have a bad vacuum actuator. The rubber is bad. I have removed the diaphram from the cable and attempted to pull the cable with vise grip attached. The cable does not pull out more than a 1/4".
I have taken the three bolt off and removed the cable from the transfer case. I can pull on the shaft the cable attached to but it only moves the same 1/4" I assume this should not require much effort to pull out and it should move more. Can anyone help?

Jack the passenger side front wheel off the ground and turn the wheel very slowly by hand while you pull on the shift fork in the front axle to see if it can engage. If it still does not engage, you will need to pull the front axle passenger side extension tube off and have a look at the parts inside.

Ok, a question about the cable to the transfer case.
 

Down on the transfer case where the cable inserts into the fork. What is the electrical connection function?

I assume you mean on the front axle. That is a switch that tells the TCCM that the front axle has engaged.

Follow up
 

I jacked up the passenger front. I spun the passenger wheel while pulling on the cable to engage the fork. No worky. The fork still only moves 1/4". Is it possible to remove the short section between the chunk and the CV axel without pulling the CV out?