Hi Chris; welcome to the board!
First, you're right; you should be able to hear one pickup with a regular cable plugged into a stereo 1/4 jack. If you plug a set of headphones into it, you should hear both pickups; one in each ear.
Second, it has two batteries, not one; and it will run through a set of batteries within a few hours.
$2,279 seems reasonable for an older S1 with no case or power supply, if it's in otherwise good condition. A power supply can set you back a few hundred, as can the case.
If it hasn't been played in a while, the pots and jack may need to be
exercised.
Does this particular store happen to be part of a large national chain? If I recall correctly, a couple members have run across an S1 with problems at a chain store that I think was in the Chicago area.
So, go back with a couple of fresh batteries, a set of headphones, and exercise the pots and jack.