The 2 prongs on a plug, one is hot the other neutral, aka utility ground. The third is earth ground and is redundant. Sometimes earth ground is your hum inducing ground loop. Removing the extra ground is an easy way to improve cheap power cords and many components. Silversmith's Jeff Smith carries one around to demo and did so here at Chuxpona.
In this case since the problem developed over time and occurs on every outlet and even when not connected to anything else this all argues for the caps going bad. Caps are cheap, the values printed right on them, making this an easy DIY fix.