Before you shout "ASB", let me just explain the scenario.
Suppose that the Falklands War never happened in 1982. For whatever reason, Argentina does not invade, but the junta still falls, and Argentina is pretty much like it is today, professional army and all that. However, as a result, the Falklands are left poorly defended.
Now, in 1998, the British discovered there was a ton of oil on the Falklands. Meanwhile, Argentina's economy was collapsing, and there was a massive nation-wide economic crisis thanks to mismanagement by the military dictatorship. The President suddenly sees something that could help ensure re-election success on a wave of euphoric nationalism, and go some way towards fixing the economy.
Argentina then goes to the UN and gets a resolution passed condemning British "colonialism", and demands the islands get handed over. Argentina now thinks the world is behind it, and gets increasingly confident. Britain refuses to hand them over. A crisis brews. Clinton calls for "negotiations"; this is taken as a sign of neutrality. And with the British never having demonstrated they could retake the islands in 1982, the Argentine General Staff assumes that it will be militarily impossible to retake them.
So in 2000, Argentina takes the Falklands and overwhelms the small British garrison. As in OTL 1982, the Argentinian troops are ordered to take the islands without killing any British soldiers, a feat they accomplish.
What happens next?