Auto trans won't shift into 3rd - just pops, lurches, and stays in 2nd

What is your question?

When accelerating, the automatic transmission smoothly shifts from 1st to 2nd, but won't go into 3rd. Instead, it winds up the RPMs, makes a loud popping sound, and lurches. Is this necessarily an expensive transmission issue (which would 'total' this aging car), or possibly something more easily repaired?