Fuzzy white stuff sounds like mealy bugs, which commonly attack indoor plants. How often do you water? Do you have any new fronds sprouting from the center? It sounds to me like it might be crown/root rot (the crown just happens to be at soil level on a younger palm like this). If that is the case and you have rot in the crown, the palm is lost. Palms are pretty susceptible to rot - particularly indoors - if they aren't allowed to dry some between waterings. Not bone dry, but at least somewhat dry.
If you have a new frond sprouting from the center, does it look healthy? From the third pic, it looks like the new frond is one you had to cut - which if that is the case, is a bad sign itself. *Gently* wiggle it or give it a little tug. It should feel firmly in place with some tension not allowing it to move much at the base. If it feels loose or wobbly rot is probably the culprit.
Sorry to be such a barrel of bad news, it just doesn't sound good from my experience with palms.
but hopefully I'm wrong!