Well, try it on a PS2, if it doesn't work on the PS2, it's broke.
It's not as if the shop needs to know it was also being used on a PC, now is it?
IMO it's not a question I wouldn't expect them to be asking anyway. It should be a case of you walk in with it and say 'It's not working', they plug it into a PS2 and check, then give you a new one.
Most places, if you simply want a replacement, won't even bother checking first.