SCSN sums it up pretty well. Though you identify the combo, you fail to apply it by buying only two Oases and Menageries. Without trashing your initial cards (or even with trashing all of the starting copper), that isn't nearly enough actions to draw a significant portion of your deck. The $2 buys at the end of the game should be ignored, as the Estates don't help any, and the Beggar's extra copper will ruin whatever hope you have with your two Menageries.
The key here is extra buys and spamming the key engine parts. Once you have most of the Oases and Menageries, it's pretty much impossible to stop you from drawing your deck and getting a significant amount of $ while doing it. By halfway through this game, you should be playing 5-6 Oases every turn, along with 4-5 activated Menagie, a couple of Markets for extra buy, all capped off with the Ghost Ship to cripple your opponent. With enough of the cheap actions, you can very reliably do this every turn. Your opponent goes for a plain Big Money deck, which should have a very tough time in the face of constant discard attacks.