The seller mentions that the remote "doesn't work now." I'm wondering if he/she is just saying that because the batteries are dead, and the person didn't think to try it with new batteries before listing it.

Many non-technical people think anything that uses batteries is broken when it stops working, when all that's actually wrong is the cells are weak or dead. This is one reason Zenith stayed with the mechanical ultrasonic Space Command remote control system for its TVs as long as they did -- they didn't want people thinking the TV was broken because the remote's batteries were dead. Kids, especially, would put up a fuss when the remote failed for any reason. "What?!
Do you mean I gotta get up to change the channel?!" With today's flat-screen sets, these kids would be out of luck in case their parents locked the TV's manual controls with a password (as can be done, I imagine, with most FPs). In a case like this, however, it's probably just as well since some kids watch far too much television (when they should be outside in the summer or reading) in today's 500-channel universe anyway.