Year, engine, mileage?
When you say it won't start, do you mean it won't crank over?
Sounds like the alternator is not charging(is the RED battery light/symbol on?).....car runs until battery drops below 9.6 volts(when voltage drops below this, the car's computer can't function)..........then can't crank vehicle(battery too weak).....overnight, the battery recovers....
Battery should measure 12.6 volts with nothing on......with vehicle running, should measure 13.0-14.5 volts(high end on cold engine, low end on warm engine)....if you rev the engine to 2000 rpm, should see voltage increase....