Easiest this is to connect a volt meter to the battery (or into main at your fuse box) and monitor the voltage when you have the non-start condition (as well as normal starting). During non-start condition, a voltage drop when you turn the key, to ~9 to 11Vdc would indicate a bad connection or starter solenoid problem. If no drop is noted, the battery/starter circuit is not your issue and it's time to look elsewhere.
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