1996 Chevy Cavalier

My car recently died on me, i was driving when i notice my head lights were diming and my battery light came on. My head lights and other inside lights slowly die to nothing then the car shuts off. I Charged the battery for about an hour and get it started up and i got it home. Ihave a brand new battery but when i hooked it to the charger it was very low. Does this soundlike AStarter problem or ALT?

Starter has nothing to do with charging system. It is either your battery or alternator. You can have both tested at most major auto parts stores such as AutoZone or O'Reilly's for free. Off or on the car, if you can get it there.

bluelightnin6 is right.
Nothing to do with starter, one without knowing cars much can tell, unless it is a design for both starter and alternator (generator).
If the charging circuitry is in good shape, it will be the alternator, w/o current generated from the alternator, your car draws current from the battery until it goes flat.
My damn GM cavalier got me replaced alternator twice within 6 months because the damn Delphi supplied crap alternators. To buy one is relatively cheap (not really cheap) but to install w/o tools, you can release the tension arm that let the belt runs thru. My damn cavalier gave me a lot of problems and costed me much good money after this bad stuff...., I just return home with it on a 2nd coolant temperature sensor replaced, it is one of the culprits that caused NO START immediately after use.