Not really sure if this was the right forum to post this in, but I'll ask anyway!

I have a Jackson Kelly with the DiMarzio Evolution set that I had a guitar store employee install for me, and I have a new Epiphone SG with Seymour Duncan's Hot Rodded set that I installed myself.

My band and I practice in my brother's room (only place the drumset would fit) and I run my Kelly or SG through a Vox AD50VT and the other guitarist runs his Kramer through a little 15W Line 6.
We put our amps near the desk where my brother's computer sits.

Now, the problem: When I play either my SG or the Kelly through my amp, in between notes, or even when there's nothing being played at all, there is a very sharp and high-pitched noise that never goes away, and sometimes, there's a "hum" (didn't know how else to describe it), even when I have the strings muted.

When the other guitarist plays his Kramer through his amp, none of that happens.
But today, he played my Kelly through his amp, and the same thing happened to him.

What could be causing this?
If it's the computer, does it matter if it's on or off? I tried shutting it off to see if that would help at all, and it didn't.
If it's the pickups, should I resolder? I double checked to make sure they're soldered in the correct places with a good soldering job (had my dad help me.)
CRT Monitors create lots of noise (frequencies). turn it off and see if that works. Otherwise it sounds like you have a grounding problem
A noise gate pedal..? Alright, I suppose I'll look into that.
And a grounding problem? What do you mean? Incorrect solder placement, or just poor soldering in general?
And, by chance, do you think it could be my cable, as well? It's somewhat a low-quality cable and I've had it for a while now.
My guitar does an annoying buzz too, but it's really cheap and I believe it to be the real low quality pickups. If I sit turn the guitar towards the amp it gets worse too. If I use the single coils* it's real bad, but it still does it with muted strings on the humbucker.