Dulled:Scuff sand it. Get something in the higher numbers like very fine paper you use on the cars. You do not want to sand off the vinyl. You just want to rough it up a bit.
Clean:You can use a spray bottle that you can buy from the dollar stores. Use bleach, Dawn and some soap powders for a quick fix. This will need to be soft brushed clean after you let it dwell like 5 minutes.
Dry: I would wait a couple days to dry out. Also now that winter is coming on, I would only paint it like after 11Am or so and not past 3PM.
Coating:Resilience by Sherwin Williams. Use the Satin finish, but build it up if by brush. If you are handy with a spray gun, you can take it off and onto saw horses. cover the area beneath it and tape off any hinges or door knobs that are not to be painted. I would apply a few coats to it. Do not try and cover it in 1 shot.
This is one way you can approach this as I have used this in the past.
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