IF you fry the thing, you WILL know. Guaranteed. You won't always be able to see it right away, but the most spectacular form of it is if you cause sparks to fly, hence the "fried" term. At the least, ESD causes an electric current to pass through the chassis and can severely damage or destroy parts of the computer. For example, you might fry the motherboard. Or the processor. Or something like that. Scary, huh? If you caused ESD, that system isn't likely to boot again.
However, ESD is easily prevented by having the computer off and the power cable plugged in and touching a piece of sheet metal inside the computer that isn't a circuit board or anything like that. The power cable being in is essential; when you touch the metal, that static electricity has to go SOMEWHERE, and if the cable is in, it goes into the wall, which is equipped to handle electric currents. The chassis, however, is not.
If I just scared the heck out of you and even my assurances don't reassure you enough, you can always get a pair of anti-static gloves. They cost about five bucks at the local electronics store. But you shouldn't need to get them; I go inside my computer perhaps a little more frequently than I should, and the only time I use the gloves is when I install something extremely expensive, like a motherboard or CPU.
As for the fan buzzing, I don't think anyone's thought of this yet, but I have had that happen to me from time to time. See, my computer box is so special (i.e. so @$%@ expensive) that it has four or five fans going in there. For a little while, I'd get this buzzing/scraping noise from inside. Lucky for me, the side of my computer box is transparent, so I could see the problem without shutting down. My problem was that a wire had gotten free of the twist-tie and was rubbing up against one of the fans. If I'd just left it there, it could have chewed through the wire's rubber casing and caused a malfunction like never seen before.
So, when you're in there, check to see if any wires are very close to or touching the fan(s). If there are some, get them away from the fans. Twist-tie them if you have to. If not... let us know.