Sounds like too much tension to me. It shifts to the easier gear first, then because it's slightly too tight, it goes to an even easier gear. I bet it's really a hard push to get it into the lowest gear. I bet it doesn't upshift really well, either. Anyway, before buying all new cables and housing, try setting it up from scratch- set the limit screws, the b-screw, then set the cable tension while the bike is on the stand. If it doesn't pop from one gear to another, it's probably time for new cables and housing.