How can I troubleshoot an intercom interference issue in a Piper PA-28?
For the wiring, you need to do several things. First, obtain the Vendor's manual for the SL 300. Next you will need to trace out the wires going to the SL 300. I suggest labeling them. 

This type of work is beyond normal pilot/owner maintenance, and I would urge you to work with your A&amp;P or avionics shop tech to get support while you debug things, and also to provide guidance as you navigate the wires, controls, etc. that might need some displacement while you work on things.

A suppression capacitor can be installed, but I would identify the problem first. Again, the avionics tech should be consulted, and any filter you install will need to be documented, and "signed off" but you probably already know this as you own the plane.

Give a better description of the sound, or a recording, and you might get better ideas on where to look.