jnicholes, I am here to 'Pump you Up"! I am here to tell you that brown roots like you first mentioned are dead, non revivable.
Second, your Phalaenopsis will survive!! No doubt in my mind you can get it to not only recover but bloom again.
Cut off most of that root system, none of it is useful. None of it! Cut off that bloom spike. Cut it all the way back!! You really do not want the plant to rebloom right now. If it does rebloom, it will most likely die. With lots of healthy roots and leaves, your plant would have tons of energy in reserve to bloom. It could take up water and nutrients and produce a nice bloom spike. BUT there are no live roots left to take up water and nutrients.
Once all the roots are gone, get some New Zealand sphagnum moss. Pre moisten it and pot your orchid in maybe a 3 1/2" or 4" plastic pot. Put a little moss in the bottom of the pot and wrap the old root stubble, that you cut back, in a ball or clump of moist moss. Place it so the leaves are just above the moss.
Keep it in medium light, no sun, nothing really bright. Think of it as needing less light as it recovers. I can safely predict that new roots will form within 4-6 weeks, 8 at the most. They will start sucking water up right away. They will grow longer, take up nutrients and plump up those leaves. It will look SO MUCH BETTER!
It will easily bloom again for you next fall. How sure am I? 99.5843965% sure that you can save your baby.
Good luck!!!
Lastly, just keep the moss moist, not sopping wet.
