I am having the same problem. It is unlikely that a new trackball will fix it.
The sensors that monitor trackball movement are built into the trackball unit, but the pushbutton is on the circuit board under the trackball. Pull the trackball out, and use a stick to push the copper contact on the circuit board. You should feel the "click" sensation. If the phone does not respond, a new trackball will not fix it.
I tried this on a good phone and my broken phone. Putting the good trackball in the bad phone did not have any effect.
AT&T tells me that my Blackberry has a two year warranty, and they are shipping me a replacment phone.
The same issue happened with my wife's 8320... we did go as far as ordering the new trackball assembly and it didn't fix the issue at all. The problem was just what Regas mentioned: the copper contact was "depressed", so she got it replaced under warranty.