2003 olds shoulette won't shift to 3rd or drive

Any check engine light?

sounds like a stretched linkage cable

not enough trans fluid...... if it slips after a trans flush reuse the old fluid its got the old clutch dust in it and the clutches will grab better....

change the coded solenoid and the reset the ECM and after a few days read the fault codes again

check trans fluid level/color. trans may have old/bad fluid in it and may need to be flushed and new filter installed.

i have a 2003 chev s-10 pickup with automatic/ 4 cyl I am not able to move shifter from park to drive i believe my shifter cable is binding
gears selection matches fine when shifting. But will not get out park go to reverse or neutral selection only drive, 3rd, 2nd and 1st
do i need to replace shifting linkage cable?

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no gears indicates that the torque converter clutch servo/solenoid s faulty
probably a disconnected wire from your working with the others

yes but you can get it less becauses the kit cost only 72 to220$ for it and its a half day labor onit any ? you can call 863 261 6116 if no answer leave a message

IT COULD BE SOLENOID PACK OR THE GOVERNOR AND TRANSDUCER OR LOW FLUID OR THE MOST COMMON REPAIR SPEEDS SENSORS INPUT/OUTPUT. ALL OF THESE CONTROLS THE SHIFTING. START WITH THE SENSORS FIRST, VERY COMMON.