Option #1 – about $100, you can buy a continuity tester for RJ45 that would test all 8 wires through the panel and tell you, as you go through each jack, if any ports are bad. You would have to make a little jack off of the back of the panel where the punch downs are.
Option #2 – again, create a little jack off the back using a short cable and a receptacle, connect a hub to it. take a laptop and go through each jack on the front, as you move the jack on the back (punching it down over and over again) – to simulate a network connection through the panel.
Either way, there isn’t an especially easy solution.
I hope that helps!