With respect to grounding, a properly grounded pickup coil will function properly, whereas an ungrounded coil will not. An ungrounded shield will not reduce noise. If your shield and pickup grounds are internally connected (which is most likely the case here), you must have a firm ground connection to that shield mesh or your pickup will not function as designed. A little solder will give you a lot of useful information. You can do this yourself. You already have solder on your pickup shield (shiny bit at the end), you just have to heat it up [EDIT: with a soldering iron!] enough to flow it onto the top of that pot. Make sure you don't have a cold joint, plug that f7cker in and test it out.