Driver side door does not close. Latch broken and door sits down below catch on body of car.

FIX CAR DOOR LATCH

Inside door mechanical issue broken

I too have had this issue. This is what I did too solve problem
step 1 spray with brake cleaner to remove all foreign materials
step 2 check operation with screw driver and door handle.
step 3 check that bar on body is aligned properly with catch in door
step 4 use large torx bit to loosen bar and align with door catch then retighten
step 5 lube catch with white lithium grease or equivalent not ( water displacer 40) problem should be solved

Door pins are a common failure on that series of Blazer/S10's. Also, another point of contention that the door faces is a sticky latch. Basically, the door latch re-latches itself and when you shut the door into the catch, it slams into it and bounces off. An easy fix is a 3 part cocktail of brake parts cleaner. Open and shut the latch with a screw driver acting as the catch and your interior door handle a few times. P'Blaster, open and shut the door a few times with the screwdriver acting as the catch. Finally, a good shot of white lithium grease. Open and shut the door with a screwdriver as the catch several times. Once you feel it is un-stuck, actually close and open the door several times. If you notice the door rising every time it catches, you MUST replace the door pins (cheap fix). If the door still has issues, replace the door latch (and since you're in there, do some PM and replace the actuator as well).

sounds like the latch is broken or the latch catch is out of alignment. you can try and spray some teflon or silicone based lube on the latch and see if it is just sticking -- some lube goes along way on moving parts. also make sure the door is lining up proper and not hitting anywhere on the frame.
but I would try the lube first,, and then look into possibly replacing the latch.

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spray the latch catch with oil or silicone to loosen the latch mechanism than stick something [a screwdriver/ pen ] that u can use to push the catch upward to open push on catch while lifting handle if catch falls back either latch spring still frozen or latch spring broken and needs replacement

will the door not return to the original position or it will and just not catch.
either way the door panel has to come off and look and see if its just a plastic clip broken or the whole latch needs to be replaced.

The latch in the door is in the closed possition most likley or the latch is broken all together. Hold the door open pull on the handle. use a screw driver to unlatch the closed catch. it looks like a sideways w that closes in on itself around the striker on the door.

Wit the door open, using a srewdriver, use it to throw the catch, then see if the latch locks into position. if it doesn't then a new catch will be required as the locking latch spring inside the latch would have broken

HAVE YOU REPLACED LATCH? IF SO YOU NEED TO ADJUST