First thing to try is to put it on a channel with known constant activity, such as a NOAA weather channel or your airport's ATIS frequency. If all you get is a hum, it's quite likely you have a shorted connection somewhere, or you've plugged into the wrong port on the PC. You need either the Line In or mic in - every soundcard responds slightly differently.
Another thing to check is your soundcard settings. Check your soundcard's control settings by double clicking the speaker icon in your system tray (some systems you need to go thru Control Panel). Look specifically at either the Line In or Mic in settings under 'Recording' and see if there's any setting that seems to boost the response (some have a 20db amp, others use extra compression....). I experience a nasty hum if the level is set way too high.
The cable may also be wrong. Some soundcards use a stereo input, others use a mono input.
I don't think you have a ground loop issue, but it's also possible. Our recording wiki has a tip or two about that....that's about all I can think of at the moment....73s Mike