Hi Judith
That looks salvageable.
First, clean any old potting medium (bark, etc.) off of the roots. Some portion of the root system may be obviously bad (dark brown, mushy), use your fingers to pull the bad stuff out (if it is yellow, white, green or silvery, or brown but firm, leave it). Then keep the plant out of any pot or potting medium for a while until the roots have a chance to dry a bit (maybe a day or two). Orchid roots are adapted to be in the air, so this will not hurt them.
While the roots are out of the medium, let's look at them to understand the root structure. The true root is thin, and is inside a thicker, spongy coating called velamen. Most of what you see that has rotted is the velamen; the thin cord that you may see as the rotted velamen is removed is the root, and may or may not be OK.
While the roots are drying, get some basic orchid potting supplies. Lowes, Walmart or Home Depot (or whatever big-box home improvement store you may have in your area) will have orchid bark for potting medium. For pots, I personally prefer those reddish, unglazed terracotta pots because they drain well; you may be able to find terracotta orchid pots with holes on the sides, those are good if you can find them. The ideal pot should just barely fit all of the roots with a little room for orchid bark. Some people like plastic pots, and they are fine, but must have many holes in them to drain well.
After a day or two, check the roots again, try to pull off as much of the remaining rotted material as you can from the root system. Some of what was mushy/rotted before will feel papery now, remove the papery stuff.
When you re-pot, here is a link to some basic re-potting instructions:
A couple things I would mention: the video recommends a mix of materials, while I have recommended just sticking with bark; that is sort of a personal choice, but plain bark or bark plus charcoal works for me. Also, he attempts to sterilize scissors with alcohol, which will not kill plant viruses; instead, heat sterilize your cutting tools by running them through a flame until hot (just the cutting tips), then cool before using.
Phal roots total mush. Desperate for advice :(
I did not realize until tonight when I got a chance to check out the roots (never even knew to and never would have had it not been for this wonderful forum and members here). I was horrified to see that there was no drainage hole (duh!!!) and the roots were immersed in water 
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