From your pictures, I believe the cabinets are a laminate and the walls are vinyl wallcovering. Both are paintable if the substrate is adhered solidly, cleaned throughly and prep'd with an appropriate primer. The key is in the cleaning and prep-ing. If not done well, the paint will peel.
From your picture, it looks like the laminate may be damaged or peeling along the top edge (maybe it's just an illusion) but if it is, this would be tough to paint over without it being noticale even with all your hard prep work.
I have seen the vinyl wallcovering painted with Zolotone - it looks GREAT!
There are lots of people that have done similar projects - you may want to read through some of the older threads (search using some key words like "paint" "laminate" "wallcovering" "vinyl") until someone else replies directly.
Good luck in whatever you decide to do.