Not mushy...well, brown roots don't sound too good either. To confirm: If the outer layer comes off very easily like a thin skin (dead velamen) and leaves a thin "string", it's definitely dead. Or bend the root. It it doens't snap like a carrot and is "limp" it's dead too. Now that you've gotten straight which roots are alive and which are dead, repot in fresh orchid mix. Be sure to cut the dead roots--leaving them there can cause fungus. It's best to try a new clean container that's as clean as possible. Find the right size to accomodate the healthy mass of roots.
To repot a blooming den, just follow the same repotting procedure--take plant out, get rid of mix, cut dead roots, put in new pot and new mix. Be careful to injure the plant as least as possible, and be sure not to break the spike! There's always a risk with losing flowers from repotting, but many times the flowers stay unharmed.