You didn't say what year you have but, the cable has an adjustment at the transmission end. You need to release the adjustment lock, adjust cable then reset lock.
The transmission linkage connects the shifting the lever in the passenger compartment to the shifting lever on the transmission. You will find the shifting linkage on the side of the transmission.
The shift linkage on your Chevrolet Blazer automatic transmission will go from the shifting handle to the right hand side of the transmission. The shifting linkage is actually a shifting cable.
Shift linkage broken or disconnected?
Transmission linkage bushings can be put on by first removing the linkage cable and removing out outer linkage cover. The bushing can then be pull out and replaced with a new one.
Several things can cause your transmission to be stuck in second gear. Broken or detached shifting linkage will cause the problem. A broken shifting for in the transmission can also cause the problem.
The first cause of the jump out from one to other gear is the loose shifter fork, which connects the shifting linkage and gears of the transmission. The second cause is loose shifting linkage itself, which connects the gear shifting knob and shifting fork. The shifting linkage and shifting fork become loose due to the rapid changing of gears from one gear to other at high speed of vehicle. The third cause is the misalignment of shifting linkage to the shifting fork.
If your pressing your brake when shifting it could be the neutral and park sensor. Or the linkage. If its the linkage you might have problems with your transmission slipping and shifting by its self or into certain positions easyly than others.
The 2001 Chevy Cavalier automatic transmission shift linkage is held in place with a swivel nut on each end of the shift linkage. Turn the swivel nuts to the left and the shifting linkage will come off. Reverse the process to install your new shift linkage.
bad linkage in shifting cable
Try to change the transmission filter, or check the shifting linkage.
The shifter linkage might be jammed or disconnected. The shifting sensor, that detects if the brake is engaged, may be malfunctioning.
Remove the driveshaft. Remove the shifting linkage. Unbolt the transmission from the Bell housing. Remove the transmission mount bolts. Pull the transmission backwards, to remove it.