Following are some thoughts on the starting problem. This is not a completed or exhaustive comment. B9t, it will hopefully give you a good start, assuming you have not yet corrected the problem.
Now onto the cranking.starting problem. I agree with the folks that say you need to start with a fully charged battery. However, before charging down that path it is good to know if you have a no crank, slow crank, or cranks fine but won't start issue. In the case of an engine cranking fine but not starting we are dealing with an issue other than the charging or starter system. But, if it is a no crank or slow crank issue we can do some other stuff that will be helpful. For either a no or slow crank situation you really need to start with a fully charged battery. If you are lucky that will be all you need, although it does beg the question about why the battery had become discharged to begin with. That is a subject unto itself. So, if a charged battery does fix the problem, it is time to do a charging system test, and/or check for a current draw from the battery when the ignition switch in in the Off position.
After charging a battery (slowly) overnight I would take it to a parts store that can do a load test to see if the battery has the capacity to both hold, and deliver a charge sufficient to crank over a start motor under load. Or, if you like to tinker and work on your own car you can get your own carbon pile batter load tester for a fairly reasonable amount. An aside, I see the newer "smart testers" are allegedly capable of load testing a battery without using a high resistance, high current carbon pile. Okay, maybe. But, at some point my Old School-itis kicks in and says nothing beats a carbon pile tester like another carbon pile tester when it comes to really testing a battery. My preference is to use an old Sun VAT-40, or even VAT-28, but those are really old and may not be easy to find - much less in working order. I have a VAT-40, which came to me with a damaged inductive lead cable. I was able to fix the cable with some baring of a wire ands resoldering it to its socket. But, I wanted a load tester that easier to carry around, just because I need an excuse for a heavier duty unit - seriously. I ended up with a Solar brand battery carbon pile based load tester from Amazon that really works nicely. The VAT-40 is still an impressive machine, and can do some things the Solar tester can't. But, for an easy to carry around test unit the Solar machine does a great job. No regrets. Here is a link for one of those units:
https://www.amazon.com/Clore-Automo...mzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc
The way to use the load tester is to connect the large gauge cables to the battery. Then turn the carbon pile dial until you are showing 1/2 of the battery's Cold Cranking Amperage (CCA) rating (or use 250 - 300 amps if you are not sure). You continue to let the battery be loaded for no more than 15 seconds. If the battery is unable to sustain 9.6 volts, or higher, at the end of 15 seconds of the load testing, the battery needs to be replaced (assuming you were testing a fully charged battery). It is that simple. If you need a new battery do not go cheap. Get the highest CCA rated battery you can for the size you can fit into the battery holding area in your car. For First Generation Mustangs I use group 27F, not 24F, as the 27F can hold more lead, which means they have a higher charge capacity than the 24F batteries. Personal choice,, plus experience over the pat 50 years.
If the battery passed, or is new, and still fully charged, and you still have a cranking issue it is time to begin to diagnose the real issue. But first, is it not cranking? Or a slow crank?
If the charging system checks out, as well as the Neutral Safety Switch for a no crank issue, the next thing to check is the battery terminals themselves to ensure the connection between the battery posts and lug terminals are clean and have nothing preventing a good flow of current. I do not like screw/bolt on terminal ends on battery cables. Too often I find the connection is poor, usually due to corrosion under the clamping plate. I far prefer the lug terminal ends to be pressed and/or soldered. Check the ground cable to make certain it is affixed to the body/frame of the vehicle, as well as the engine. It is critical the engine and body/frame are connected one way or another with a high current capacity cable. In the First Generation Mustangs there are two general kinds of negative cables that one can use to help ensure there is a good ground to both the engine and the frame (yes, I know the Mustangs are unibody, I use the term "frame" loosely). To clean the lug end terminals I like to use a found wire brush designed to clean both the batter posts and the inner circumference of the lug terminal ends.
Now onto the cranking.starting problem. I agree with the folks that say you need to start with a fully charged battery. However, before charging down that path it is good to know if you have a no crank, slow crank, or cranks fine but won't start issue. In the case of an engine cranking fine but not starting we are dealing with an issue other than the charging or starter system. But, if it is a no crank or slow crank issue we can do some other stuff that will be helpful. For either a no or slow crank situation you really need to start with a fully charged battery. If you are lucky that will be all you need, although it does beg the question about why the battery had become discharged to begin with. That is a subject unto itself. So, if a charged battery does fix the problem, it is time to do a charging system test, and/or check for a current draw from the battery when the ignition switch in in the Off position.
But, after charging a battery (slowly) overnight I would take it to a parts store that can do a load test to see if the battery has the capacity to both hold, and deliver a charge sufficient to crank over a start motor under load. Or, if you like to tinker and work on your own car you can get your own carbon pile batter load tester for a fairly reasonable amount. An aside, I see the newer "smart testers" are allegedly capable of load testing a battery without using a high resistance, high current carbon pile. Okay, maybe. But, at some point my Old School-itis kicks in and says nothing beats a carbon pile tester like another carbon pile tester when it comes to really testing a battery. My preference is to use an old Sun VAT-40, or even VAT-28, but those are really old and may not be easy to find - much les sin working order. I have a VAT-40, which came to me with a damaged inductive lead cable. I was able to fix the cable with some baring of a wire ands resoldering it to its socket. But, I wanted a load tester that easier to carry around, just because I need an excuse for a heavier duty unit - seriously. I ended up with a Solar brand battery carbon pile based load tester from Amazon that really works nicely. The VAT-40 is still an impressive machine, and can do some things the Solar tester can't. But, for an easy to carry around test unit the Solar machine does a great job. No regrets. Here is a link for one of those units:
https://www.amazon.com/Clore-Automo...mzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc
The way to use the load tester is to connect the large gauge cables to the battery. Then turn the carbon pile dial until you are showing 1/2 of the battery's Cold Cranking Amperage (CCA) rating (or use 250 - 300 amps if you are not sure). You continue to let the battery be loaded for no more than 15 seconds. If the battery is unable to sustain 9.6 volts, or higher, at the end of 15 seconds of the load testing, the battery needs to be replaced (assuming you were testing a fully charged battery). It is that simple. If you need a new battery do not go cheap. Get the highest CCA rated battery you can for the size you can fit into the battery holding area in your car. For First Generation Mustangs I use group 27F, not 24F, as the 27F can hold more lead, which means they have a higher charge capacity than the 24F batteries. Personal choice,, plus experience over the pat 50 years.
If the battery passed, or is new, and still fully charged, and you still have a cranking issue it is time to begin to diagnose the real issue. But first, is it not cranking? Or a slow crank?
More to come in in another post, hit the 10,000 character limit.