It sounds like its wants to start and its not the battery !
How do you know you need a new starter ? on 2004 Mitsubishi Galant
Find your starter and starter solenoid and while turning ignition tap firmly (but don't beat on it) on the starter and solenoid to see if the engine turns over and starts. Be very careful the vehicle is immobile so not to get hurt doing this. Yes, you will need an asssistant to do this.