I have been recording guitars for quite a few years now and thought I'd drop in on this First, a CRT is short for Cathode Ray Tube which is the technical term for the former technology of screens and television set. They are notoriously harmful for em interference. LCDs, like the one on you laptop, tend to be less noisy though I need to play facing back my LCD screens when I play with my Les Paul.
I have not seen your environment so I don't know how your speakers are plugged in/positioned but this also can have an adverse effect. Do you have stompboxes/switchboxes between your guitar and your DI box ? If so you might want to check the gains on those too.
Now there are two schools of though as far as volume goes and quite a few religious wars have been started over this but I'd tell you to dial in your tone the way you want to hear it and if it is at 5 then it's good (11 is good too ).
A quick trick, is to put a gate in your effects chain, basically a gate will not let sound through below a certain threshold therefore eliminating this humming completely. I don't know what effects pedals/plugins you have so I don't know what gates you have in your arsenal...
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