Now that you are sure it's a 350 turbo, I'll throw something at you. If you look at the transmission, where the dipstick tube goes into the trans case, there should be a cable coming out that goes to the carb. . This if I remember right is called a throttle detent cable. If it is not connected either at the carb. ,or inside the transmission,the shifting could be affected. Inside the trans.the cable is connected to a valve in the valve body which is the brains of the transmission.
Another thing, it sounds like the truck had some other things done, maybe previous owner installed a shift kit in the transmission. If the check balls under the valve body plate are not in the correct position this could also be part of the problem.
good luck and let us know the outcome.
