2001 Mitsubishi Galant Will not start

I turn my key, all the lights and bells come on, but nothing happens when I try to start it. I can hear it clicking when I pop the hood, but if I put it in neutral and push it a few feet, then throw it in park, and then turn the key, ot cranks right up. Its an automatic transmission tho. The car has a new transmission within the last year, and I jusy had the spark plugs changed about a week ago. I also noticed if I havent drove it since earlier the previous day, it usually cranks right up, drives perfectly fine. Then when I turn it off, let ot set a while and try to start it again, thats when it has to be pushed to get it started, and after it does start, it runs very rough, tries to die at a stpp, and idles extremely low at red lights/stop signs.