Well, there are certainly a lot of possibilities and questions, huh? I think that John Kerry was both a.) inept enough and b.) close enough to say that it's possible a Democrat could have won that election. The problem, of course, is that the other Democrats running lost to a guy as inept as John Kerry.
Well, first the main contenders.
a.) Howard Dean - I think the debacle in Iowa in 2004 proved that Dean really didn't have the chops to run and win a national campaign. There's always the chance that whatever lightning in a bottle he caught June-December 2003 would come back, but it didn't seem likely. He was a candidate ultimately who energized a lot of people who could do a lot of good work for a guy like Obama, but not one who stood a real chance of winning on a national scale.
b.) John Edwards - Well, let's go out on a limb and assume that his cheating would not be a factor (obviously, it hadn't happened yet, and I'm assuming that Rielle Hunter wasn't part of a trend that nobody has discovered so far). He seems like a candidate who would stand the best chance to beat Bush - seeming young and energetic at a time the White House seemed more than a little stale. Ultimately, though, I would guess his lack of gravitas could spell his doom against Bush-Cheney.
c.) Dick Gephardt - I don't really care for him, but he could have run a winning campaign if he really ran hard on his labor support, and avoided the wedge issues that Bush deployed against Kerry. A Gephardt-Vilsack ticket wouldn't have excited any coastal liberals, but it could have pulled Iowa, Missouri, and Ohio into the Democratic column without giving up more than maybe Oregon and New Hampshire. That would be a 279-259 win for the blues. A Gephardt presidency, though, is outside my depth.
d.) Wesley Clark - He never really emerged at all in the campaign, somehow managing to win Oklahoma in the primary. He's such a wild card still that I don't know what to do with him: either his lack of skills displayed in the OTL campaign will just sink him, or else he'll hang on to some of that "I'm a general" legitimacy and maybe bring a few, sigh, "security moms" into the fold. He could run the Kerry+ campaign, hanging on to just enough votes in Ohio to tip the scales.