I'm assuming you pulled the carpet back to check for any screws at the bottom? My first suggestion would be to use a utilityi knife and cut around the edge to score any paint/caulking that may have it stuck in place, although there is really no need for caulking, but I've seen stranger things in construction Not sure what else may be holding them in place other than that.

Hmmmmm. Well you did all the obvious - have you tried sticking a screw driver in the vents and prying??? It could be that you might need to take a utility knife and run along the edges to loosen it from the wall., It could just be really stuck w/dried paint - or I guess it's possible the builder might have used an adhesive to really secure it to the wall but that seems like major overkill. You want to take them out BECAUSE??? You are 1) replacing them or 2) going to paint them???

You may have difficulty finding replacements at the home centers for these. Here is a link that may help you out. There are many suppliers for baseboard diffusers such as you have. Some come with their own wall frame, some require the wall to be trimmed out such as yours appears to be. http://www.installerstore.com/Triangular-Bas...

We cleaned, lightly sanded and spray painted our vent covers. They look like new!

We have "huge" metal vents on the walls and wood floorsRustproof primer and spray paint. Drywall was the only other alternative. A big box store doesn't have vents that large. It all worked out though!