Normally we would pursue the rough running as a simple misfire and look at the ignition system, fuel supply, EGR system, and compression / valves, but if we're to assume the dead battery is related, a good suspect is the generator. Specifically, since the '87 model year, GM's redesigned generator has caused a real lot of trouble. Due to its design, they develop a lot of huge voltage spikes that can destroy the internal diodes and voltage regulator, and interfere with computer sensor signals.
Charge the battery at a slow rate for an hour or two, unplug the small connector at the rear of the generator, then drive far enough to see if the rough running has cleared up. If it has, suspect a defective diode in the generator. You'll need a professional load tester to see how much current the generator can deliver, and if "ripple voltage" is excessive. If one of the six diodes is defective, you will only be able to get exactly one third of the generator's maximum rated current. 30 amps from the common 90 amp generator is not sufficient to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down.
If testing confirms low output from the generator and it needs to be replaced, replace the battery at the same time unless it is less than about two years old. That is the key component in damping and absorbing those harmful voltage spikes, and as they age and the lead flakes off the plates, they lose their ability to do that. Failure to replace the battery often results in four to six repeat generator failures.
Thursday, January 22nd, 2015 AT 3:05 PM