You have the classic signs of a compromised battery.I can't speak either on what type of tests they did, or how effective those tests are or are not, other than they had me do numerous things while a machine was connected to the battery, including rev the engine, turn on the AC, turn on the high beams. It was the most in-depth test I've had done on it yet. I had it tested once a week ago or so at another store and the guy just hooked his machine up to the battery, pressed a couple of buttons, and it spat out a piece of paper saying the battery needed charged. Problem there is I've tried to charge it, and it won't take a charge.
I'll check out the negative battery cable info you provided. That may be what it is. At this point I'll take any lead!
Let me echo the words of my learned colleagues:
Replace battery immediately. If you're still covered by the three/36 bumper-to-bumper then this is done at no charge by your dealership.
If not expect to pay ~$200 for a quality battery. Plus install.
Furthermore, the advice on using a booster cable to jump the ground cable was spot on.
The midtronics battery testing machine that is required dealer equipment is one **** of a unit but way too costly for a shop that doesn't specialize in batteries.