it doesn't go into 4hi when I hit the button

Those two things arent related.The actuator probelm is 2 or 4 wd, high and low range is something to do with the transfer case.Start by checking all fuses.Do the range lights ever blink? Might need to put it in diagnostic to see if the PCM has stored a code. Dont need a scanner for this.
Turn ignition off for at least 6 seconds. Find DLC (diagnostic connector) bottom of dash near steering column d/s. Should be a diagnostic pigtail, (orange wire at DLC terminal 13), ground this wire, turn ignition to run position (engine off) and see if the indicators on the switch flash.If all blink once and stop, no codes. Otherwise count the flashes, there will be a 3 second delay between codes. Get back to me with results

The range lights blink twice when I ground the terminal you suggested. I believe before this test, the lights would also flash twice while changing ranges although not entirely certain. I know prior to changing the actuator motor, there also was lights flashing. I understand now that the two problems are not related but changing the actuator motor did solve my problem going from 4hi back to 2hi. Just some FYI.

Code 2 is for the motor on the transfer case.Need to check all wires to the motor and connectors for damage/corrosion first. The TCCM (transfer case control module) Is behind the right kick panel. Need to check wiring from there to the switch and from the TCCM to the motor

Well, I was leaning toward the problem being of an electrical sort but I don't know what wires are suppose to be hot and when because I was lacking an electrical schematic for that circuitry. I have one now thanks to a friend but from what I gather of what you are suggesting, maybe I should just be concerned with continuity from switch to TCCM and TCCM to motor...correct? Also, you said the TCCM is on the right side kick panel...is that what I hear "clicking" when I change ranges? I was hearing it but couldn't find it. Thanks for telling me....it was driving me crazy looking for it.

This is the same problem as a the blazer that I am problably going to buy here in sweden has. I would very much like to know the answer to this problem when you find it out.

This seems like a very good forum, not easy to find help with american cars here in sweden sometimes, thanks!

/Erik