Why is my car having trouble starting with a new battery?

I had this problem. I discovered that the nut which clamped the wiring harness to the alternator was loose which caused intermittent connection from the alternator to the car's electrical system including the battery. Tightening the nut down fixed the problem.

you should check for voltage drop on battery leads (measure at battery post not clamp) as I have had this in the job I do.