1996 Jimmy 4WD Problems

I have two problems that may possibly be related:
For past 2 years during hot weather (never below 80 F, but common above 90F) the transmission seems to not want to shift. Engine revs up and sounds like a jet, but does not accelerate for a period of time and when it does, the tac goes back down and it runs fine. This has been happenng for about two years only in the summer.

Yesterday I was on a really bad road and pushed the 4WDHi button and continued, not realizing that it hadn't engaged. It resulted in getting stuck in a mud hole but fortunately some friends came to the rescue with a comealong after a phone call.

If the vehicle is in drive moving or not, when the button is pushed nothing happens at all. If the vehicle is in neutral and the button is pushed, the lights on both 2WD buttons blink 3 or 4 times and I hear a faint sound from behind the dash that sounds like a solenoid, but 4WD does not engage.

Yesterday after getting out of the hole, I pushed the 4WDLo button when in neutral and the light stayed on, but it didn't feel like 4WD was engaged. The light went back off when I pushed the 2WD button standing still in neutral.

Anyone have any idea what might be going on here with either of these problems, or do you think they are related?

For the tranny it sounds like the valve body needs replaced...

For the 4wd:

1st Check vac actuator under battery tray for tears, or leaks, and that the vac hose is connected. Replace if found

2nd Check vac hose leading from vac actuator to vac switch on transfer case for cracks and dry rot. Replace if found.

3rd Check remaining 2 hoses from vac switch on transfer case for dryrot or cracks Replace if found.

If all of the above are fine, disconnect your negative battery cable for 1/2 hour then reconnect it. If your 4x4 works after that you probably have a failing TCCM (Transfer case control module)

If that doesn't solve it, it's most likely the encoder motor

hi im new to this but i need help with my 4wd. i have a 97 jimmy sle with 4.3 v6 vortec and when i push the 4hi button i can hear the transfer case from under the truck clicking. so i go to a parking lot with sand and gravel and only the right rear wheel spins. no 4wd. i changed the vacuum switch on top of the tc today. before i connected the rubber lines i checked for vacuum and one of the lines was sucking in but the other two werent. i also checked the actuator under the battery and i could manually push in the rubber part about 1/2 inch or so. but i cannot check for vacuum when truck is running because damn battery is right on top of it. what should the actuator do when its in 2wd and what should it do when in 4wd? thanks for any help
p.s. i really need 4wd working because winter is coming in a few months. thanks in advance.