2000 Buick Century TRANSMISSION WONT SHIFT BEYOND SECOND GE

HI hOW CAN I DETERMINE WETHER THIS PROBLEM WILL CAN BE FIXED WITHOUT REMOVING TRANSMISSION. COULD IT BE A FILTER THAT IS BLOCKED, OR A SOLENOID OR STUCK VALVE? OR IS THERE A SENSOR THAT MIGHT BE MALFUNCTIONING. A BUICK DEALER WHO CHECKED IT TOLD ME TO JUST PUT A NEW TRANSMISSION IN IT FOR $3200.00 WHICH I DO NOT BELIEVE IS WORTH THE COST ALLTHO THE CAR IS IN MINT CONDITION