If the pot does not have a drain hole, be aware that adding too much water can cause roots to rot, as deadly as not adding water for such a long period that roots die of desiccation.
The leafless trunks do look dead, and it would be easy to determine if you have a strong pruner that can cut into them. Cut small sections from the top until you find healthy, whitish material inside.
Whatever happened has killed 2/3 of the plants trying to grow in this pot. I would repot it, meaning removing the old soil, rinsing it off of the roots, trimming the "pancake" of roots you'll likely find at the bottom of the root ball, replacing with new soil and using a pot with a drain hole in the bottom. This would allow an opportunity to remove the dead trunks, if you determine they are beyond hope. I will be doing this soon to my many potted Dracaenas, as I do almost every year, because they always start looking less happy when the roots run out of room to grow and are suffocating in a strangling pancake at the bottom of the pot.
Dracaena plants are sensitive to tap water chemicals, especially fluoride, which does not evaporate, regardless of how long water sits. Whenever possible, using distilled, rain, &/or condensate from a dehumidifier or A/C should produce a noticeable difference and if used regularly, eliminate concern about tap water chemicals building up to toxic levels in soil.