I would start with all the primary battery and ground connections. Make sure the connection from the battery on the starter is clean and tight. Obviously check both battery terminals for being clean and tight. Check the ground connection to the block.
You said it has a rebuilt engine. When the engine was installed did the ground that goes from the back of the head to the firewall get re-connected. This is very important and will cause exactly what you are talking about and I have seen it many times. On that car it was probably a steel or copper braid and it usually was on the passengers side head and bolts to the firewall. If it is not there, you need to install one. The absence of this will also put more of a load on the other grounds and can eventually cause complete failure or a fire.
The bulk head connector is also another place to look but it would not be my first choice.
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Last edited by T-bucket23; 02-27-2009 at 07:16 AM.