As long as you are grounded and clean you can touch the electronic components as much as you want. That towel you use its likely to cause static though, so you should probably get rid of it. Before touching the components, make sure you are clean, since left over grease/grime could short components (unlikely, but it is an easy precaution to take). The more likely problem is static, especially since you cover your case with a towel (which is half of the ingredients needed to create static electricity). Before touching the components, just ground yourself on the case, and you should be fine.
I am an electrical engineer, but I must admit that my current job doesn't involve building and designing circuits. The last job that involved designing and building circuits was a little over ten years ago, so I am a little rusty on everything, but everything I said above is pretty basic and should be accurate.