Last time I watered them it took so long for the soil to dry which I suppose means that their roots are not in good shape? Should I cut their branches and put them in water? The croton has lots of little buds on it.

It's difficult to answer that without a photo. Sometimes, depending on humidity levels, it can take longer for a plant to need watering again. That would be normal. But if it goes on for an extended period, then maybe the soil is too retentive, not enough light, or something is attacking the plant etc. Are the plants sitting next to each other? You can always remove the plant from the soil too and take a look at the roots and put it back in the pot if you're worried about roots.

Here is the croton.

I wonder if it had spider mites? Do you see any webbing anywhere? If it were me, I would take pruners to it and cut back the wood to 4-6" so all the dead was gone. If you see webs, spray the whole thing with insecticidal soap, including the soil. I would then leave it alone and see what happens. It doesn't look good but since there are buds, hoping the pruning will force new growth (and it will be bushier)

It had last year. I persistently took them out till they disappeared. But I'll get some insecticide. I'm thinking its roots may not be in a good shape so cutting a stem and putting it in water may prevent it from total death.