My car doesn t want to start?!

I drive a 2000 Honda accord! I have a brand new battery, just about a month old now! Some times the car will start and itll be fine! The times it doesnt, there isnt a clicking as if there was a bad battery, theres just the ever so slight sound of the fuel pump pumping fuel! I checked my connections and everything seems to be perfect! Could it be a solinoid or the started?

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