[AussieinNC]

Th350 is a detent cable only, not a pressure feed cable for line pressure like a 700R4.

Take detent cable off the carb and slowly pull it out, you should feel the lever in the trans push the valve in, then a little more pressure to get to the last cable out position.
If you can feel the valve move, the cable is most likely not installed correctly inside the trans.

Have someone hold the accelerator fully open and pull the detent cable fully out.

You should be able to slip the end of the detent cable onto the pin on the carb throttle plate.

I have seen folk not put the square end of the cable fully into the square hole in the bracket...it must fully seat inside the bracket.

I have also seen the inner cable out too far in the square connector base....push on the tab on side of the square block and push the inner cable towards the front. this should let you now connect the detent cable...

To set it...have someone push gas pedal to floor, then pull outer detent cable backwards to remove all slack in the inner cable.

Pics of your setup will help