Correct me if I'm wrong, but I don't think the Sponsorship Scandal really got going until Fraser issued her report and Martin subsequently called the Gomery Commission… in February. If the election is in January, Martin and the Liberals avoid the worst of it; sure, he'd likely face some criticism over pre-empting the report, but without a numerical value to put to corruption, it's all just abstract, about the principle of the matter rather than anything concrete.
The Conservatives are interesting in this scenario. True, they didn't pick their leader until March IOTL; but ITTL, if it seems like Martin is gearing up for an election for January, I expect they would handle leadership differently. Perhaps, with only a few months between their merger and a federal election, they have a provision where Harper directly ascends to the Tory leadership, with a review/convention scheduled after his first election. That certainly doesn't feel right to me, but at the same time… if you simply don't have the time for an election… maybe that's the least bad option.
Either way, I foresee the fabled Martinslide everyone dreamed of (or feared)— in 2004 and beyond. An election around the Great Recession (2008-2010), I think, would be massively in the Liberals' favour; Martin can point to his work as finance minister as not only lifting Canada out of recession before, but also for being directly responsible for the reason Canada was relatively spared the effects of the Great Recession. With that in mind, I can't see them not being returned in another landslide, and I think that has some massive knock-on effects; because it means the Liberals would have the branding of being fiscally prudent and responsible, and that's a massive blow to a Conservative Party that, ITTL, is struggling to define itself or its message. And if Liberals thread that brand of fiscally conservative/socially progressive… well, that's a hell of a place to be.