Steve Vai. Now there's one boundless talent! Thanks for your posting Megastar.
This is an excellent topic that we all get plauged with (sooner or later). Since we all have (or will have) our problems with it, I would like to take the liberty to write about a few things I have learned to help control this beast. I believe the best thing to know first, is exactly what we are dealing with, and up against.
The Topic: HUMMMMM.
Megastar, hopefully you'll get to read this before you lay down big money on a nice guitar cord. Not saying a cord is not worthy, but it's usually not the typical solution.
Identifying what is causing a component to output humm is a good place to start. Keep in mind that there is no absolute solution I am aware of for the complete elimination of humm output from an electric guitar, however it's likely that you can successfully reduce it to nearly inaudible levels.
In most cases, it's origin is ~60 cycles sourced from line current. There are many scenarios to effect the device that is polluting our sound. From reversed polaritys and improper or lifted grounds, to mismatches of impedance, using wrong value or cheap capacitors, blown capacitors, popped diodes causing voltages to not flow as intended.
A guitar pickup is specifically made to detect the string vibrations in it's tight magnetic field. We can't blame the pickup, because it's only doing it's job, and if the pickup were less sensitive, sustain would be comprimised. The humm is commonly the resultant from the pickups being bombarded with interference from an outside source.
Nigel's solution is natural. It could only make sense for the immediate moment to stop the emmission from the source. It seems odd however, for a computer CRT to dicharge enough to have to turn it off. A good idea might be to verify this device's ground. Naturally, you must have all devices properly grounded which specify grounding. If your wall receptacles are only 2 prong, that could be it as well. Don't expect an adaptor to do the trick because the box inside the wall that the receptacle is screwed into might not be grounded. Without proper grounds, you can anticipate humm to arrive as if it was by invitation. Another suspiscion might be a leaky flyback transformer, as they don't last forever. If you rest a very large stainless steel salad bowl covering the back of the CRT and hear an audible difference, your tube has got some problems. This would be RFI (Radio Frequency Interference) and is easily detected by the pickup coils, even in small amounts. Pickups are very suseptable to different types of interference. They are so sensitive that it is the leading reason for electric acoustic guitars to have their pickups designed to detect vibrations from the bridge / soundboard instead of the string, since phosphor-bronze strings require an even greater amount of sensitivity to detect vibrations electromagnetically.
An additional approach is shielding.
Shielding protects the sensitive input hot. The better it protects, the less likely the signal will be affected by outer elements. Many guitarist even spray the inside part of their instrument that houses the electronics with a metal spray that you can get wherever they sell Printed Circuit Board project kit ie. electronic surplus and supply stores. You have have noticed that the pickgard/cover on strats have metal strip tape on them. Also be sure to not remove the casing and/or tape from the pickup itself. They wouldn't make extra expense of more parts into the build if it would yeild no benefit. Pickup bezels are especially important because they are part of what confines the shape of the electromagnetic field closest to the strings. Really good input cables have great shielding properties. Twin copper braid plus copper foil is the best stuff I have seen. No noise from your cable while using that stuff. Very low loss too, but it costs.
Well, I hope a helped a little, hopefully someone else will add to your subject posting with some more ideas.