Battery issue or something else

Does that car has a battery cut-off switch? Contact might be partially burned or not all the way on. Also you.might want to try the battery directly onto the starter to.diagnose if there is a partially broken cable or connection along the way.

 

Grab bag of ideas...

Bad new battery? It happens, the failure rate is higher than most would expect. Try a known good battery to rule this out.

The large connector in the engine bay that is disconnected for the engine out needs to be cleaned, maybe some corrosion inside?

Is the starter old, maybe the solenoid is on the margin of failing?

 

Connect up a voltmeter using long wires to the positive on the starter solenoid, see what volts you have. Now engage starter and see the volts.
Next connect the volt meter up to the power cable on the starter- you are looking for a volt drop

 

If you are getting a voltage drop, then it's not the battery at fault. There is some faulty high resistance connection between the battery and the starter. You should be able to use your voltmeter to trace down the fault.

 

If the starter is going in and he is getting a voltage drop it can be the battery, if the battery is on its way out a big demand will try and pull the volts down. On a good battery it will deliver to the load with a small drop but a old battery will not maintain the volts. Put the headlights on and see if they go out when the starter engages.

 

To me, a "voltage drop" means that the voltage at the starter is substantially less than the voltage at the battery, whilst the starter is being engaged. This would not indicate a faulty battery.

 

The voltage at the starter terminal is the voltage the battery is putting out under load. You cannot have 2 voltage reading on a common line. It might be a 12 volt battery but its volts drop under load if it is not in a good condition

 

You can have different voltage readings on the same line if there's resistance from bad wiring, or a bad connection between the battery and the starter.