I would definitely not divide this plant or remove back canes in its weakened condition. This plant looks like it needs all the help it can get and removing its energy stores won't accomplish that.
This den looks like either a phal type, an aussie native type (a kingianum hybrid of some kind) or perhaps a cross between the two. It bears some Den biggibum characteristics. If you have not already done so, go to the orchid care section of this forum or to
AOS | Members Only Area and get yourself a good culture sheet on phal type dendrobiums. Read it and let us know if you have any questions about their culture.
Remove all of the dead roots (even if that means you don't have many left) and pot it up in a good bark mix. Tale Olives tip that healthy roots are firm and crisp while dead roots are mushy. Dead roots will usually pull right away if pulled on gently. When potting, select the smallest possible pot that can accomodate the roots. Give it the culture/conditions indicated on the culture sheet.