STARTING PROBLEM

2002 Dodge Intrepid 2.7L, 86,000 miles that is giving me starting problems the past week. I go to turn on the ignition and there is nothing, no instruments no power fortunate this is not all the time. Sometimes I will turn the ignition on and all I will get is a click I will then wait and try again and then another click and sometimes I won't get anything - no power nothing. I know it sounds crazy but the majority of the tiime when I hit the battery the car will eventually start. I had the battery replaced back in January along with cable terninals. I drove from California to Texas in Febuary without any problems. The voltage on the battery is good. I cleaned the battery post and checked to make sure the cable terminals are tight on the battery post but I'm still having problems. Last time messing with the car I got it started and cut the car off and heard a small desending whinning noise while the hood was up. I don't know what that is or if it has anything to do with what's going on. Your reply is greatly appreciated. Thanks