What do the battery cable terminals look like? What does the ground lead's lug look like (at the bolt where it fastens to the chassis)?
If those are ok, then I'd suspect the engine to chassis ground jumper or the alternator. If its the alternator, that will show up by watching a voltmeter as you drive, if system voltage is not stayihng above 13.8 or so when driving, the alternator is not charging right.
I had weird issues iwth my Graphite, and I think it was the ground(s). I fixed it for $15 by doing this:
GO to store, buy a generic ground cable like this one:
Buy a ring lug to fit the smaller wire, a lug that will fit the battery ground bolt at the chassis next to the battery.
Remove the battery ground cable from both the battery and chassis ground bolt - throw the cable away.
Grab your new battery cable and crimp the lug onto the smaller wire. Fasten this lug to chassis using the original bolt. Connect the Battery terminal to the battery.
Now, run the BIG LEAD to the engine block and find a suitable bolt that you can TIGHTEN DOWN GOOD and connect to the block. I used an alternator ground bolt.
YOu have now connected the battery, chassis and engine block together to eliminate the block to chassis cable from the picture. (Doing this is easier than trying to verify the integrity of the jumper under the car.)
If the jumper was the issue, you are fine now. If it is NOT the issue, you have spent 1/2 hour and $15 - since I'm not there to help you troubleshoot, this is about as good as I can do.