Does it crank over at all when you shut it down and restart? Or does it just click but not crank?
If it's just clicking, sounds like your clutch safety switch could be bad, or your ignition circuit could be bad?
When you test for voltage with the car started, turn all accessories off, including the stereo, and see what the voltage is sitting at on the battery. Then turn all of your accessories on, even A/C, and see if the voltage jumps up from what it was sitting at with accessories off. This would check the charging circuit. If there isn't much of an improvement, then you've still got grounding issues somewhere, or a defective alternator.