Determing if your problem is in the shifter or in the transmission would be the easiest, and you can do it.
You dont say how the shifter feels. Is there any play in it, etc? Under the car there are two rods that go from the shifter to the trans. They come out from under the heat shielding and then one bolts to the trans, and the other bolts to nearby, IIRC to the trans' case. If either of these are bent, missing, disconnected, it would cause problems, and if the left one is disconnected (the one that actually shifts the car) you wont have any shift pattern at all, except for the lockout of reverse.
So in other words, is the shifter stuck in fourth, etc?
Oh, and $3000?! Seems a bit steep, especially when you hear of people getting their clutches changed out (same labor) for a third of that.