PlayStation Pause Problem

I've bought a few more old PS games over the weekend. The list includes Die Hard Trilogy, Alien Trilogy, Dino Crisis, Duke Nukem: Time To Kill and Syphon Filter 2. Actually, that's all of them! I'm having an issue with Die Hard Trilogy though - when I start a new game the PAUSE function keeps launching, its maddeningly interrupting. I had the same thing with Tomb Raider II and after taking it back and exchanging twice gave up on it and swapped it for something else. Having the same thing happen with another game leads me to think there is something more consistently wrong. Is it the controller? Should I try with a non-dual shock controller?