Why does my car intermittently start? No problem codes or messages.

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Car was fine then one month ago decided not to start. Dash lights come on normally in run position but when I turn key to start just check engine light and no sound at all. No codes, no messages, no nothing. Bought and installed new battery, car started and went to store. Came out and car would not start. Tried again, car started. drove twice since then and then car doesn't start. Tried to start it 3 different days in one week and it would not start. Went out yesterday to try it and it starts. Still no codes or messages that everyone is talking about. Oh, I did take it to the shop after the first time I got it started again and they said battery and cables seem fine and they can't tell what the problem is unless it doesn't start again. How can I get this fixed without it costing me a fortune? Scared to drive it anywhere.