#1
I have a very weird problem that i cannot lay my finger on.

I usualy record stuff at home before i lay it out to my band and afterwards record it in a studio or other semi-pro location. The problem i have is this. I use a very cheap mic, and it never gave problems (i dont have to have great quallity as long as its not horible im OK), lately however i have this weird background buzz when i record. Adjusting the volume of the mic wont help at all, in fact i discovered that when i MUTED the mic it still had the same recording volume... i tried muting everything else, but it still buzzed. Now i know my gear is crap, but the thing i cant grasp is why my mic is still recording when i put it on mute?! how can that be??
#2
might b a poor ground, try openin' up ur mic cables and one of the 3 is not connected to the clip that holds the cable on, that might cause it. Just get a noise gate. Bam.
#3
Most of the time when you have that kind of humming it's caused by the magnetic field generated by the computer screen (assuming it's a CRT). It affect guitar pickups more than microphones but if it's a cheap mic it might pick up on it. But this does sound like you might have a bad cable somewhere. It could also be that you have poorly shielded cables and you're running them next to your power cables.