There are fancier ways, discussed elsewhere in this forum, of restoring plastic involving various polishes, scotchbright pads, 3000 grit sandpaper, etc...but I don't have the time for that in my life. That's why I stick to Simple Green and 303. Don't rush on fixing up your heater box. It took...
Looks like you need some new foam on that heater box. I used SOR foam from several years back and was happy enough with it. Lots of the other grommets and screws in the kit didn't match up very well though. You can source some of your own foam, apply some some 3M spray-on headliner...
Clean with Simple Green. Set the concentration level to whatever is necessary for your level of grime. Protect afterwards with Aerospace 303. You don't want too much shine as that will attract dirt.