"But it is still cutting off and mostly not starting at all... " Does it crank strongly when you try to start it? If so, it's not the battery. If not, it could be a bad connection or ground. In a car that old, it's not unusual to have some corrosion interfering with good electrical flow.
Check the wiring everywhere you can. Sometimes just pulling a plug apart and putting it back together is enough to re-establish a good connection. Look for white powdery fluff which can signify corrosion at a connection.
Now there are many reasons why a car won't start, so you should check for spark and fuel, too.
Report back with your findings, positive or negative as there are lots of people who might chime in here with more suggestions.
|