Battery issue?

The logic is not sound. This sounds like the alternator has failed. It's job is to recharge the battery after cranking the engine, and to supply the entire electrical system while driving. When that doesn't happen, the car runs on the battery until it gets too far run down, usually in less than an hour or two. That is long before it is totally dead.

The place to start is by measuring the battery's voltage, first with the engine off, then again with it running. Tell me what those two voltages are, then we'll figure out where to go next.

Also look at this article. It covers much of what we're going to be doing:

https://www.2carpros.com/articles/how-to-check-a-car-alternator

If you need help using a digital voltmeter, start with this article:

https://www.2carpros.com/articles/how-to-use-a-voltmeter

They're using one with "auto-ranging". That's an expensive feature you don't have to have. Harbor Freight Tools has a perfectly fine digital voltmeter for around $7.00. I can help you set it up if necessary. You can find similar meters at Walmart or any hardware store.

Let me now when you have those two voltages.

Something doesn't add up. Exploding batteries and needing a jump from another vehicle don't involve the ignition switch. It sounds like the jumper cables may have been connected backward. That will cause a huge shower of sparks and can ignite the hydrogen gas batteries give off. We talk about that all the time, but I've only heard of that happening once before, many years ago. I'm also concerned that it ran okay for two weeks. That normally would not be the case if there was a problem with the ignition switch. Is it possible the car was the victim of an incompetent previous owner?

I'm still suspicious the charging system is not working correctly. The system on your car is very simple, and easy to diagnose, especially when you have me to help. If you continue to have problems, please get me the two voltages I asked about, and come back to see me. I've had a number of similar models, and still have two 1980 Volares with the same charging system.

Later in your description, it does sound like the failure to crank could be due to the ignition switch. For that, the first step is to look for additional symptoms. Does anything else turn on with that switch, like the dash warning lights, radio or heater fan? If everything else works properly except the starter, check the ignition switch adjustment. It's mounted on top of the steering column with two 5/16" screws. The mounting holes are slotted to allow for adjustment. If that doesn't pan out, the entire starter system can be broken down into four circuits, each with a corresponding test point at the starter relay socket. Those four tests are best done with a test light. I'll describe them if that appears to be the direction we need to head.

If everything seems to be working properly, please give me an update in a couple of weeks.

Dandy. Warning. I'll be at the Iola Old Car Show swap meet in Iola, WI for the weekend, so you might not hear from me until next Sunday or Monday. Don't panic if I don't reply right away. We won't leave you sitting in a pile of tears.

The 12.4 volts points to the battery is roughly half discharged. A good, fully-charged battery will read 12.6 volts. When it's considerably higher right after charging or running the engine, that is due to what's referred to as "surface charge". That's due to electrons that haven't gotten absorbed into the plates yet. They're floating around in the acid and cause those false readings. When that is a concern, just turn on a load for a few seconds to remove that surface charge. Headlights work best. Turn the lights off after five to ten seconds, then recheck that voltage.

Even though the voltage is a little low, it is not nearly low enough to indicate the battery has a bad cell. The next reading is the same battery voltage, but with the engine running. The charging system should develop between 13.75 and 14.75 volts. If that is what you find, that system is working and it's just the starting system we have to worry about. This is where we start at the starter relay's socket. That takes considerable time to type the instructions, but the tests are very easy with a simple test light. A helper will be needed to run the ignition switch during those tests. In the meantime, don't get too carried away with taking things like the dash apart. There's nothing in there that will cause this problem.