It may have needed a starter, and especially a new battery, but generally putting new parts on is poor diagnostic strategy. Sometimes it's the most practical way, but this case should be relatively easy to solve with a multimeter and test leads. It sounds just like you're saying, the electrical system collapses, the voltage just isn't there anymore, so get a helper to turn the key, while you check the voltage, first at the battery, then at the starter, then at various other places based on what you find.
If you want better explanations, check some youtube on voltage testing starters under load. A Powerprobe is a DC voltmeter with a long cord that makes this sort of thing easier, but not needed if you can think through how to do it with a multimeter.
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