It would be really interesting to find out why some computers emit this noise and some do not.
It has to do with poor grounding and poor system design. Ground currents are flowing in the motherboard and/or chassis.
In a well-designed system currents return from a source on a dedicated, local return path. In a poorly designed system (i.e. typical cheap consumer PC) return currents flow over multiple return paths. This causes differences in ground potential at different points in the system. Now when you connect a cable to a different system there will be a potential difference between the two systems and current will flow in the ground of the cable. This current causes an electromagnetic field which goes right into your pickups.
For example, consider a PC with a typical low-cost consumer hard drive. This hard drive has poor power supply filtering (to save $$$). When the drive is active it pulls current from the power supply. The current has a noise component due to the poor filtering. Ideally this noise returns on the ground wire but, often, it returns via a different path, typically the motherboard or chassis. Due to the finite resistance of the ground this noise current induces a noise voltage on the ground wrt to earth. Same thing happens with signal sources, often times worse. A signal current is sent to a receiver and the return current takes some circuitous path back to the source through the chassis, etc. Remember, current always flows in a loop (Kirchhoff's law). If you source current it has to return somehow.
Now you connect this PC to an Axe-Fx (which is designed correctly and whose chassis is very close to earth potential) via a cable. The potential at the PC side is noisy wrt to the Axe-Fx side. This causes noise currents to flow in the cable ground. Now any current that flows in the cable has to return somehow. Some of that current returns by going through the Axe-Fx power cable ground and back into the PC via its power cable ground. Now you've created the infamous "ground loop". A loop with current flowing in it creates a magnetic field (Ampere's Law). Your pickups are magnetic transducers and convert that magnetic noise field into an electric noise voltage.
When it comes to USB, sometimes the easiest solution is to try a different port. The ports on the back of the PC will be at a different ground potential then those at the front/top/whatever.
USB is inherently flawed in this regard. It specifies the cable be connected to system ground at both ends. But you can't remove ground safely as you risk damaging the controller ICs.
This is one reason optical protocols were invented. They break the galvanic connection between systems. Ethernet works well too because it is differential signaling with a fault-protected PHY and no ground connection between systems.
Now all this is different than the $%(* stupid case window BS. Cases with windows are the dumbest idea ever and should be illegal.