Can sick phals grow new roots?

[Cello09]

Someday I will learn to stop buying orchids at grocery and hardware stores... but until then, I will keep nursing the ones I have bought there back to health!

I'm fairly new to this. My first orchid is doing well, but ever since I lost a pretty mini phal to root rot (I blame the grocery store for letting it sit in too much water), I'm a little paranoid.

This Phal noid had some rotten roots when I brought it home. I trimmed them off (sterile scissors), treated with fungicide, potted in "Better Gro" bark mix, water about 1-2 a week with fertilizer as needed, and keep it in a fairly humid room. When the blooms started drooping, I checked out the roots and they look dry and dead. I there any way to get it to grow new roots?