Thanks for the reply. The seller said he tested the controller with the system just before he shipped it out and it worked fine, and I have no reason not to believe him. Just odd that it arrives to me and does not work. Upon further testing, having this defective pad plugged into the unit ALSO disables the second player port as well. VERY odd. Something is up with it, that is for sure.
EDIT: Tested on another PS2 AND tested with a PS2-PC USB adapter. Does not work with either.
So, confirmed, the controller is oddly just "dead". The only time I ever encountered something like this was with a new Atari Jaguar controller about 15 years ago. Guess these things (very rarely) just die sometimes. Now I have to hope the seller compensates for the fact that I had to buy a new controller for the system. I still can't believe these things still go for $25 plus tax....