Car won't start, but battery,alternator and fuses are all good. on 1999 Mercury Cougar

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I replaced the starter and still nothing.The lights,radio,etc. work but it doesn't make a sound when you try to crank it. Could it be the ignition switch? Any other ideas?
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Is the battery new? because a battery with one bad cell will light some lights and the radio but won't have enough amps to engage the starter or power up the ignition system. Start with that and trouble shoot from there
Left the battery on a charger over night and still nothing...the battery and alternatr are about 1 year old.