I was having the same issue. Has nothing to do with the cable type you're using (i mean, besides it being a micro usb cable, obv).
Connected my droid razr to my comp and it wasn't responding. All you need to do is restart your phone. You do this by holding the power button and the down volume button at the same time for 10 seconds. Once it restarted, it's been connecting to my comp no problem. Charging and accessible.