I recently worked on a Galaxy (Two button), don't know if yours is the same but be very careful, I tested the battery and it was fine, thinking it can only be the battery I got a replacement, fitted it only to find it still did not work, I found this very strange, I eventually figured out that there is in fact TWO batteries, when I removed the first there was a metal plate beneath which I thought to be the contact plate but once removed there is another one beneath, once this one was replaced all was well!

Yes red LED is supposed to illuminate when button is pressed!

Martin