Have you tried to just pry it out with a screwdriver or something? It may just be stuck. If you pop it out and there's no spring action (button stays in when depressed again), you may have a broken spring.
There really is no way to open up the e-brake to repair a broken button mechanism, so will probably just have to be replaced. Replacing the e-brake is fairly simple once you remove the center console.
If needed, contact member "itsnotanova" for a replacement e-brake. He parts out a lot of these cars in the classified forum and I'm sure he has one. His prices are also the best in the world!
