It is unusual to have a hardware problem with the RSP, unless it has been electrically overstressed, e.g.
lightning strike or static build up, or operation in close proximity to, or shared with a transmitting antenna.
To isolate the problem try using a different USB port, or with and without a powered USB hub. If possible also try a different USB cable (any cable rated USB 2.0 should work).
Windows users should look in Device Manager and confirm that the RSP appears in "Sound, Video and Game Controllers" with no warnings. Mac Users can confirm that the device appears in System Report.
See also
No Devices Found
If all looks OK, please review the Software section of this help guide, otherwise check the "I think my device is damaged" button.