A number of things could be wrong and you need to eliminate each as possibilities:
1) bad connection at the battery. TEST: check battery posts for corrosion. If no corrosion is evident, leave the hood up, try to start again, and then go to your battery and see if you can detect if a battery wire has gotten warm. If it's warm or hot to the touch, your wire has corroded inside the insulation.
2) Your starter has locked up and has drained your new battery. TEST: turn on your lights and attempt to start your car. Your lights should dim considerably when you try to start, and go almost if not all the way off. If your lights do not go dim or out, then you have an open connection between your battery and your starter. Check wires, check your relay.
3) Your battery charging system isn't charging your battery while you drive and you think everything is okay when it isn't. You might take a short drive to a nearby store and even come back just fine, but next time find you can't start your car because your battery hasn't been recharging while you drive.TEST: best way to is to have your charging system tested by an auto parts store like Auto Zone- Once you regain your mobility with your car, drive there and they can test your charging system and your battery on site.
Another option exists, but it's been eliminated by electronic ignition. On older cars, it's possible that the spark system in terms of coil/capacitor is faulty and the battery is what has been providing the spark to your cylinders and you've been running down your battery that way. You'd check your coil (not likely to be faulty, but possible) and the capacitor next to your points inside your distributor cap (usually the culprit)...but if your car has electronics on it, this possibility isn't an option.