Intermittent engine starting

#1
Need a little help on a 2009 Corolla. All of a sudden the engine won't start when cranking. The thing is, it does this intermittently. I can crank and crank on it and it will sound like it is about to catch but it never does. Then I let it sit for a day and come out and crank it and it starts just fine. However, when it runs the RPM's will fluctuate between 500 and 1200.

I initially thought it was the fuel pump so I bought a new one and installed it but same problem. I also suspected the fuel filter but on the Corollas the only fuel filter is a sock on the bottom of the fuel pump and I replaced it so that isn't the problem.

Any suggestions on what might be causing this issue?
 
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