Backdash Hardboard ~ Paint?

The backdash "hardboard"

The "package tray".

needs to repainted

See here for info on repainting soft parts. And be advised that REM make a nice new one (paintable to match) if yours winds up being unsalvageable.

What should I use to seal that back down

Lightly sand it smooth with fine-grit sandpaper, wipe away the sanding dust with a slightly damp cloth or a tack rag, then hit it with a couple coats of Workable Fixatif (comes in a spray can from a good art-supply store).