I haven't actually done any research on this, but I'm guessing like most devices made these days, they're not made to be repairable. Unless you're pretty handy, you might be able to find someone to send this off to to fix (lots of people offer services like this on ebay). You would have to find replacement buttons, most likely out of another defunct device, cut them out and put them in your Nook. Getting the thing apart without breaking it is usually half the battle.
My suggestion would be to either find a good used one (good luck with that) or get a new device that will last a few more years until it breaks.