Fans spin, but very slowly and weak

I traced (I think) my overheating 2005 Neon down to bad fans. Both the cooling + condenser fans have voltage at the plugs, and spin - but only if you tap the blades and start them spinning! Also, they spin very slowly, not fast enough to cool the engine and it still overheats when you are stopped for a few minutes in traffic. Will worn bearings cause a fan blade to spin very slow and weak? Also, when should the cooling fan spin - when the engine gets to a certain temperature? A worker at Auto Zone said that with the AC on, booth fans should spin. Without AC, just the cooling fan. Another thing - every 15 0r 30 seconds or so, I hear a loud "click" and the AC fan gets a sudden burst of speed and the engine shudders (jumps) at the same time.