if your line-in from your mixer is going over a power supply or AC cord it will hum or buzz. mic cables aren't as prone to AC but its never a good idea to have them cross.
be sure that you power strips are actually grounded. in fact make sure you don't have floating ground or hot ground. sometimes AC is installed by knobs that don't follow "the code" or are in a hurry and don't check their work. older homes and offices often have wiring done that way. a less then $20 tester will tell you if you have a problem.
http://www.tripplite.com/products/static/ct120.cfm
sometimes a power strip will go bad. if the MOV or has been spiked it could be leaking to ground causing a buzz. try a different one just to be sure.
clean up your mess. if you have a rats nest of cable you will have a buzz. you have to be a neat nick if for no other reason then to save time.
the power supply in your computer may be the problem. cheap or old are always suspects. laptops can also be plagued with buzz and when they buzz try unplugging from AC running on battery to see if it goes away.
finally, cables themselves can be problems. XLR cables, for whatever reason, are finicky bastards. unplug and re-plug each cable until the buzz stops. when it does replace the cable. if it buzzes again, check the mic. it may be damaged.
it might also be your board. turn down every level. then one by one turn each one up. if you find a channel that is buzzing move the input to it to a different input. if it follows the problem is not in the board. but if it stops there you go; that channel is the problem. clean the level knobs if you are so inclined otherwise you're board shopping.
finally... I got a new phone patch. when I plugged it in the whole board was full of noise. turns out the patch has Line level out and I had it plugged into one of the Mic pre's. Duh. Turning the gain all the way down solved the problem. Sometimes there's a Mic/Line switch.
