For Console: I presume you have consoled into other switches before, and that your terminal/computer/cable has been used successfully on other devices. The 3600 series needs to have 9600,N,8,1 settings (which is very standard for serial console settings of many devices).
Static Shock: Is your environment extremely dry? Like 5-10% humidity (or less). If so, get some humidity in the area. Humidifier or some other method.
If those don't fix the problem, I suspect you have bad hardware, and it will need to be replaced.
