I'm wondering if your beloved plant is a Croton (Codiaeum variegatum).

The brown bits - roots perhaps, might have developed rot. I'm puzzled about why the plant would fail to drain with all the care you've been taking.

Possibles: the drainholes are blocked. (New pot needed perhaps - but you might need to downsize if the plant actually has got root rot.)

The soil structure has broken down and the original drainage has closed up in the pot. A change of soil is in order.

The plant is in a cool spot and it's not pumping water fast enough to dry out the mix it lives in.

The roots have been dying back - or entering a rest phase - for a while and they're not active enough at the moment. (Older roots may be brownish. Dead roots are often 'flat' in appearance and break off very easily. They sometimes look almost transparent. New and lively roots can be cream or white - particularlyat the tips.)

You could put it back into a warm and bright place with enough pebbles in its saucer to let the air get underneath and the last of the drenching to go. After that, your usual winter care will probably be enough. (Water once a week or less - just enough to keep the mixture from drying out completely.)

Do check out that the drain hole/s are free of roots.

When you repot, add LOTS of grit (perlite, small aquarium gravel, etc.) to the soil so it'll drain fast in future, and try to not use lots of peat (most 'potting' soil is full of it) in the mix, but good compost instead. You can't do much now except stress it further, so put it in a bright place (I'm pretty sure it's a croton) and give it time to recover. Crotons are also subject to spider mites. Your description of the 'white things' (Perlite?) that turned brown may mean nothing except the water stained them with 'mud'. But if you have other white things that are fuzzy, then all that water brought on mealy bugs and you may need a fungicide to get rid of them, but allow things to dry out first (which will help anyhow).