Hi,
You can get a terminal cleaner at any parts store. They are really inexpensive. However, at this point, you can use a fine grade sand paper. Something like 220 grit or finer. I have also used a wire brush gently to clean the corrosion. As far as the baking soda, I know that neutralizes acidity, so it shouldn't hurt.
As far as them being tight, that is very important. The starter places a large draw on the battery. If the connection isn't good, it may not work, which is happening for you.
Just clean both the terminal on the battery and the connector where the inside attaches to the battery terminal and make sure they are tight.
https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked
Let me know if this helps or if you have other questions.
Take care,
Joe
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Friday, June 25th, 2021 AT 5:04 PM