Could be a few possible issues, such as a dirty input port. Might want to clean it out with some WD-40 on a Q-tip.
The cable could be picking up AC noise, if it is close to the computers Power Supply unit. If you is near any AC cables, make sure you cross those cables. or move them as far as possible not to pick up this AC line noise.
if you have a second sound card, could try using that. one card for CoolEdit, the other for the streaming program.
Another might be to use a program designed to capture streams.