2009 Infiniti G37 all the lights interior go on but the car won't turn over

Im having the same problem, So I own a 2012 g37x coupe, got 156k miles on her, recently replaced the transmission and radiator as my radiator leaked antifreeze into my transmission, following that I haven't had any problems since about 2 days ago, I go to start my g and won't turn over but it was cranking a bit. I went to auto zone and bought a new battery as I figured mine was 4 years old time for a new one... meanwhile 160$ later and it works for a day which is today.. went to got gym worked fine started right up and when I go to leave it won't crank over at all, just a click, all electronics work, lights, ect, but yet my car won't turn on, I go go back an hour later and still won't turn on, my battery isn't dead but yet it won't start up, won't even turn over the motor at all, I just get a little click when I press on button... if anyone can help if would be greatly appreciated before I bring it to infiniti and they charge me loads of money just to replace things that are only going to work for a day.