I don't think it's too hard to imagine in broad strokes what Gore would have done.

Any President would have attacked Afghanistan after 9/11, but Bush then used the patriotic spirit following 9/11 to lead an invasion of Iraq to depose Saddam Hussein, because it was clearly something that he (and his advisers) had wanted to do for a long time. Going after Saddam was personal for Bush: "After all, this is the guy who tried to kill my dad."

I think that Gore would have similarly used 9/11 to further his personal goals, but in Gore's case it would have been global warming and energy independence. Gore did not campaign on a tax cut, so he may have tried to raise taxes to fund a large investment in domestic infrastructure and clean energy technology.

I don't know if this would have shown any results by 2004, and Gore may have lost reelection while being attacked for not dealing with Saddam, for raising taxes, or if the economy was struggling, but hopefully there would have been some technological progress to show for it. President Jeb Bush or John McCain would then have probably canceled all those investments and invaded Iraq in 2005.