My indoor Yucca Cane looks like its dying or diseased?

Since it has a white substance, and the "mushy" feel, it sounds like it has mealy bugs. It looks like a white substance, but it's actually the bugs and they suck the plants juices which distresses other leaves, as well. You can get a systemic insecticide which will eradicate the infestation. Since your plant is in such distress, consider getting the insecticide quickly.