Ps2 controller problem ?

I bought a ps2 and plugged the spare controller in to play a game but it's not working. The light between the sticks is on, the select and start button works and so does the right analog stick. But none of the other buttons work, the shapes, l1 l2 r1 or r2 and none of the arrow buttons. Is there anything I can do to fix it? Surely it's not dead if the mentioned buttons still work?