1998 Chevrolet Malibu Past Week Car Been Starting Hard Yesterday Would Start

so for the past week the car has been starting hard and yesterday it would not start at all. i got nothing when i turned the key, but the lights all work and electric windows worked. i bought a battery thinking it was that, but no. i have been told altnerator, but no the battery symbol in the dash is not on. i have been told fuel filter.
what should i check next? could it be the altenator or fuel filter.