Should car still run on alternator with ground terminal off battery?

One of the first things I said was I took it to AZ and it tested good according to them..

I tend to agree. To do a proper test "at home" you really need at minimum some method of loading the system, and this is traditionally done what is known as a "carbon pile." You CAN find these occasionally at garage sales or on CL. There was one advertised locally the other day. I already have "a couple" and damn near bought this one!!!

http://spokane.craigslist.org/tls/5223987868.html

FIFTEEN BUCKS for a battery load tester!!!



You can, however, "improvise." One way is to leave the headlights on for a period of time, depending on how good the battery is, 1/2 hour or so. Then see if the alternator will maintain at least 13.5 to the battery.

Please read the shop manual. This is the BEST traditional source of info. You can download them free at MyMopar

You can do a "full field" test and get some idea of whether the alternator will put out enough. Depending on whether you have a 69/ earlier, or a 70/ later system, will dictate how you get battery rigged into the field.

Of course if you have an aftermarket alternator and or a "one wire" this is more difficult.