On one leg or two legs?

Hanaleimike - While your idea of running separate grounds all the way to isolated/separate grounding rod sounds interesting, it is both dangerous and will likely violate your local building code. It's also not legal to work on your own electric panel without a license, although many ignore that.

Wiring a home with two isolated ground rods may also void your homeowner's insurance should you have any sort of electrical problem.

Are they on the same leg of the main power....(i.e. did you skip a breaker when you installed your new wire?

Why did you share the ground...that's something that only electricians use to save money on cable and to avoid having to pull multiple cables. Sharing the ground is OK (you want all the grounds coming to an outlet box to be grounded at the outlet box, but you should be running separate neutrals for each line back to the main power distribution box.

My guess, for what it's worth is that you have multiple ground rods. The two at the main panel are correct...but that one separate, even if connected to the main grounds may be the culprit.

OK....before you kill yourself and us....pull out your amp and take it to an audio store...or high end used equipment seller....or just a friends house who has some halfway decent speaker (almost anything costing over $100 will do).

Connect the amp with no input to their speaker(s). See if there is a hum and if it changes when you touch the amp case. If it does....fix your home electrical so it's up to code and get your amp fixed.

If there is no hum...come back and we'll work on the problem.