The 1973 cars, by any GM manufacturer don't have ballast resistors in the system. They rely on a nickel wire that is encased in a cloth covering covered by a plastic covering, that goes from the starter solenoid to the positive side of the ignition coil. There are only a few things that can go wrong with this wire, which are all quite rare, but easy to diagnose. Since you have put 12 volts to the ignition coil, then we can conditionally rule out the ignition switch, ignition coil, and the ignition points. This leaves us with only a few things to check.
1) Has the wire come loose from the ignition coil, or has the terminal end been broken off? Loosen the nut, and then retighten to make certain that there is a good connection.
2) Checking the wire at the starter solenoid, for the same problem as mentioned in number 1, and doing the same loosening and tightening of the nut.
3) Using an ohm meter, check the continuity of the wire from the starter to ignition coil. The wire should be disconnected from both ends to do this test. It should have high resistance since it is dropping the voltage from 12 volts to 6 volts. This is done, so the points are only switching a lower voltage, to keep them from burning out prematurely. GM discontinued this wire at sometime in the 1970, and they used a resistor built into the coil.
4) If the car has a tilt column, the ignition switches sometimes come out of adjustment. Does the ignition switch have spring tension that returns the key to the run position when you let go when it starts?
Finally, you mention that you installed new batteries, might you have disturbed any of the auxiliary wires that might have been attached to the battery cables? I know that on some of my cars, there is a positive wire that comes off the battery cable that goes to the voltage regulator. Not having the luxury of being there to personally examine the patient, diagnosis is difficult to say the least. If I have a 1973 factory service manual, I would have checked the wiring schematic for a more accurate information as to where to start checking. Going from memory, there are a few cars that used a terminal on the ignition switch to supply the coil after the engine has started, and when you turn the car off, that terminal looses power. There is a strong possibility that this is something minor, but tracking it down is going to take some detective work.