Car will some mornings and not on other mornings

When you replaced the battery did you clean the terminals. Make sure the terminals are tight. Maybe your starter motor is on the way out

How well does your engine crank over? Does it crank over easily when it starts? When were your spark plugs last replaced? They should be replaced about every 30,000 miles. Does your check engine light stay on while driving? If so, go to a mechanic and they will scan for codes. Make sure your using good fuel in your tank, and if it is on cold mornings your car won't start, its not a bad idea to buy a bottle of HEET or preferably Seafoam to add in your tank to prevent fuel line freeze ups. Make sure your fuel filter is changed between 5,000 and 10,000 miles and don't run your vehicle below 1/4 of a tank if possible to extend the life of the filter.