No Clue 1990 Help Please

My mother owns a 1990 Buick Skylark. The battery is brand new and the alternator is fairly new, a year, maybe two old. The car won't start right. When she turns the key, it trys to get the belt spinning but can't quite get it going. It even slows down the longer you have the key turned. I'm not sure what's wrong with the vehicle. If you could help, we'd surely appreciate it.