What do mean when you say it won't start? Do you mean the engine turns over and doesn't start or do you mean the starter isn't turning the engine over? Another bit of helpful info is what year is your car and does your car have an automatic transmission.
If your car isn't turning over and you have a new starter you should check is the connections of the ground strap that goes from the starter to the chassis. The ground strap contact points get corroded or the strap strands get corroded and break which causes enough of a voltage drop that the starter won't.