Belinda told Darius that Kenneth was not her type, that she was just being nice to him. No way is she the type to stay at home while her friends partied, as Kenneth had said to Darius. People with deep crushes often misjudge any kindness done to them by the object of their desire. They probably never really ever dated, but in Kenneth's very creative but emotionally immature mind, he thought they had a relationship.
Perhaps he was the one who crashed into her house in the first place and killed her. I think the story is suggesting, by the wording of the newspaper ad, that he did go back in time and tried to rewrite history - but maybe he didn't travel back far enough and was already in the car (the second time) when the car was about to crash. Maybe this time, with foreknowledge, he was able to slam on the brakes sooner and only caused minor damage to her boyfriend's house. What triggered the first, fatal accident, which in turn triggered Kenneth's devotion to mastering the art of time travel in order to erase regrets and correct past mistakes? Perhaps, in unaltered time, he had been following Belinda home one evening, after work, saw her with her boyfriend, freaked out when his illusions were shattered, slammed his foot on the gas (again perhaps without realizing what he was doing due to his highly emotional state), sending the car smashing into her (or the boyfriend's ) house, accidentally killing her. He seems too mild-mannered to have wanted to actually harm Belinda.
I think Kenneth did travel back in time, did change what happened to Belinda, and maybe now he wanted to go back again to make more changes? When Darius confronts Kenneth with the news that Belinda is alive, he exclaims that obviously his previous stint at time travel had therefore worked. I find it strange that he would not have immediately tried to find this out the results of his time-travel intervention upon his return, for himself, if he was that obsessed with her.
And why advertise for a "side-kick" to go along with him back in time again? To alleviate loneliness? To fit in with the heroic image he had set up of himself as a Doctor Who type hero? Maybe he had gone in search of Belinda when he returned from his first trip back into time and seen that even had she lived, she would not have chosen to be with him. Perhaps he was subconsciously hedging his bets? If, during his second attempt to time travel and change things, he couldn't make Belinda fall in love with him, at least he would have his faithful sidekick?
Actually, I don't think we should over-analyze this movie: this movie is all about the ability to suspend your disbelief and accept that reality - and the past - can be altered, and that not everything is as we think we are perceiving things to be..... Hey, we all have regrets, but one way to rise above them is to acknowledge past mistakes and make sure we don't repeat those same mistakes. Our mistakes and regrets hopefully teach us to be kinder, better people.