I'm sure no expert, but I think you've got a good chance with the part that broke off.
Be careful about watering from the top, my oncidium twinkle I rotted off two new growths when I first got it, because I was letting the top part of the media get too wet.
Does it have any roots? If so, I'd just dunk the pot in water, being careful to not let the water level get too high (I do it just until I see water starting to show in the gaps in the top of the media), and keep the water well away from the new growths.
That's just me though. Once I started doing that, I *touch wood* stopped having issues with the new growths rotting.
How cute are the twinkles?! I have two, my first time with them and one is in spike. I'm deliriously excited!