1995 Buick Century Stays in gear

I am not clear iif car is put in drive and you drive down road if it shifts in in all gears. But if this car has a cable from throttle control on engine to transmission it can fray inside cable causing shift problems. If the only problem is it will not go into first then the arm going into transmission may be sticking or bent you can lube thier on arm. I am assuming fliud is ok.

If you put the car in drive it takes off in 3rd gear and does not shift. If you put the car in 3rd gear it takes off in 3rd gear and does not shift. If you put the car in 2nd gear it takes off in 2nd gear and does not shift. If you put the car in 1st gear it takes off in 2nd gear and does not shift. Fluids are all full. It did throw a code as the check engine light came on but I wasn't able to retrieve it. My plug-in is the OB-2 or 2 row plug but I could'nt find the 2 plugs to have it read out (flash) and theres only 3 plug-ins. 2 are over/under to the far right and 1 is at the 3rd position to the left on the bottom row.