97 blazer 4x4

There's something seriously wrong in the transfer case or controls. It seems the rear driveshaft is locked up, and the front wheels are driving. The driver's side rear tire is skidding because it's trying to turn backward - rear passenger rear tire is going forward and rear differential has no option but to turn the driver tire in reverse (driveshaft locked). DON'T TRY TO DRIVE IT. Get it checked out and fixed.

Wow. A snapped side shaft sounds serious. If you lift the front end of the truck, (or the rear end for that matter) the wheels will appear to be counter rotating, it is the way a differential works. If you turn the left wheel forward, the right wheel will turn backwards, and vice versa.
When you change to 4wd the front end does make a rather loud clunking sound as the gears engage. You should therefore change while the truck is stationary, then slowly move forward or back until the 4wd engages, then take off.
If your truck went OK on ice, it should go as well on pavement, just don't try to engage 4x4 while moving.

Check all the plastic cowlings and air dams to make sure they are not loose and rattling in the wind when you drive down the road. Check the exhaust system for any broken or loose hangers. Hope this helps.

Could be CV Shaft or Hub Bearing as well. Jack up the front of the car, support with Jack Stands and check for play in wheels/hubs/bearings/linkage by grabbing wheel at 3 and 9 o'clock positions for tie rod ends and steering linkage, then 12 and 6 o'clock positions for bearings. You should barely be able to feel play. If you think it is more than acceptable climb under the car while someone else performs the tasks above. Turn wheels for excessive brake noise or out of tolerance discs. Out of tolerance discs will cause premature brake wear and cause pads to move around in the caliper sometimes before starting to grind. Finally, and what I think you're hearing/feeling is the CV Shaft. Grab shaft, move around feeling for excessive play in joint or splines on each end. Turn steering all the way lock to lock and turn wheels at each lock, forward and backward, feel/listen for clicking/popping. Most of the time you can quickly easily diagnose bad CV Joints in a parking lot by slowly, safely driving in a circle forwards and backwards making the joint noise more pronounced. If it is a CV Joint, my advice would be to spend the extra few bucks and replace the whole shaft while you're there. Its quicker and easier requiring less specialty tools to complete the job.

replace wheel bearings or check for feathering of tires

clicking =replace axle, then drive to see if grinding still there

It sounds like a problem within the front differential, possibly broken spider gears. If so broken gear shrapnel may be jamming that wheels output shaft.

the 4wd module is bad and the chain sounds stretched in transfer case there may be a leak

Could be ball joints are bad. But if its a 4x4 the cv joint half (axle shaft) is bad.

under the battey compartment is a lever that runs on vacume unhook the cable from the vacume plungger u will first have to take the battery and battery compartment out once u get the cable unhooked have someone start ur truck and then pull the cable under the battery box that goes to the 4x4 unit dont pull too hard u may pass up the sweet spot that locks in to 4x4 they may have to go to reverse to drive a couple of time while u r pullin on the cable itr will click forward bout a half inch when it locks in if ur 4x4 works after this u will need to replace the vacume plunger or do like i did and pull it till it locks in and tie it off to sumthin n go wheelin.... lol