Check your battery cables. That's a common failure mode and cheap and easy to fix. The cables oxidize inside the insulation with no external sign. This failure mode can be temperature dependent, as the break may be reconnected by expanding/shrinking/sagging/stiffening wires and insulation. Any cables over 10 years old are suspect.
How to check the cables. After you recharge the battery, connect a voltmeter set for DC volts to both ends of the cable, then have someone try to crank the engine over. If you get more than a half a volt or so across the cable, the cable is shot. Note there are two cables to check: the positive cable from the battery to the starter, and the negative cable from the battery to the alternator bracket.
You also want to make sure the ground strap is connected between the engine and the firewall so the ignition switch and the starter agree on what zero volts is.
Here is where it is:
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