What does a shielded PC do that wouldn't be good for the amp?It won't do anything bad for the amp, but I believe Jim was just saying that he suspects an unshielded cord stands a greater chance of changing the sonic character of your system in the direction you prefer than a shielded cord. I agree.
When you say "install a 20 amp dedicated branch circuit" do you mean on the circuit breaker panel in the basement and how will that change the sound?This refers to having a breaker in the panel and wiring from the breaker to the outlet that powers the system that is dedicated to the system, and powers nothing else. It is considered to be good practice from a sonic standpoint, and often seems to be sonically beneficial, but how it will change the sound in any particular case can't be predicted with any certainty.
Presently the amp is just plugged into a surge protector extension cord along with 6 other things. Is that bad?If it's an inexpensive surge protector that is intended for general purpose use, it could very well be having adverse effects on the sound, to some degree. If that is what you are using, at some point you may want to research past threads here about surge protectors and power conditioners. As an experiment, it may also be worthwhile to see how the system sounds with the integrated amp plugged directly into the wall outlet, while the rest of the system is plugged into the surge protector.
FWIW, I've had good results with this BrickWall surge protector I used to use, and the Audience aR2p surge protector/power conditioner I presently use. (The latter used in combination with a Wiremold UL210BC power strip to expand the number of outlets). There are many other choices that would be as good or better, of course.
Good luck. Regards,
--Al