When they crash into the barrier between platforms nine and ten (and Hedwig makes a noisy fuss about it), Harry and Ron attract the attention of Muggles at King’s Cross. Unable to follow the rest of the Weasleys to platform nine and three quarters, Ron and Harry miss the Hogwarts Express. Desperate to get to school, they decide to fly the bewitched Ford Anglia. The car’s invisibility booster is faulty; the boys mostly keep the car hidden above the clouds, but they have to fly lower periodically in order to make sure they are staying with the train. Several Muggles spot the car by the end of its flight. At first, Harry and Ron are exhilarated by their situation, and enjoy eating candy and basking in the sunshine. But after a few hours of their long trip, the novelty wears off and they become uncomfortable. As they finally near Hogwarts, the car starts to malfunction.
Ron operates the car with silent wand taps. How he does this is not explained. Would this have been Alohomora, or is the car set to recognize the Weasley family wands in place of keys? Is the series of taps a way for an underage Wizard to legally cast a spell?
Harry later learns that Dobby was responsible for closing the gateway to platform nine and three quarters early. Blocking Harry's entry would not have been a good strategy if he and Ron had not been the very last people to (try to) reach the platform. Did Dobby have other plans for other situations? Even if Dobby had something to do with causing the Weasleys and Harry to be running quite late, he couldn't be sure that the rest of the family would go through before Ron and Harry. If one or both of Ron's parents ended up stuck with the boys, they would have found some way to get them to school.
It is unclear why Molly and Arthur didn't come back to find out what happened to the boys. Molly must have been frantically looking all over the platform on the other side, and when the train started leaving, one of the Weasley parents would have almost certainly tried to get back through the barrier. The logical explanation is that they couldn't get back through and didn't dare Apparate into the Muggle part of the station.