An auto car on a tow dolly?

Pull the alternator and the battery. Take both down to the parts store like oreillys or autozone. They can check both on their test bench and tell if one or both are bad. On our camaro when the battery got a bad cell it would trip sensors, lights on the dash saying that the anti lock brakes and traction control were going bad. A $30 recon battery from the local wrecking yard fixed that. On my powerstroke ford when the same thing happened it was my alternator. Both are as you know part of the charging system. My camaro was a '99 and my ford an '04. Just to say that these computer managed rigs rely heavily on a stable input of volts and amps to run their systems.
I'll take off the alternator and take it down to em, I know the battery I put in it is good so the alternator is the candidate.