I'd try the following things in this order;

1) Check and clean all engine grounds. Clean the connections on the engine and the connections on the other side of the wire. You may want to replace the negative battery cable which btw consists of 2 metals. You can always check the resistance of this.

2) Check resistance of spark plug wires or replace. You don't mention that these were replaced.

3) You may be getting spark but not enough spark. Try replacing the entire distributor assembly (which includes the distributor cap). The pickup coil and ignition control module is housed inside along with other sensors (TDC, etc) that control injector timing. They Hayne's manual (not the greatest i agree) has ways of checking the ICM and coil.

Your solution is certainly just around the corner and is probably something simple. If all else fails, I'm sure Honda could find it. An almost working car would be hard for me to through away. Good luck!