the balancer has numbers on one part of it (for timing the motor). if you bump the motor around, you will find the numbers on one part of the balancer. now if you can spin that without turning the motor, ah yeah, it is bad. i dont think that is it. if it was that gone, you would have some killer vibrations, i think.
if you look from under the car, you can see the balancer real well. you will see the rubber o-ring (elastomer) type of thing around it , toward the middle. that is the rubber that Michael is talkin about. needs to look real nice. the balancer is held together by this ring. if one part is sliding, the offset (balance) of the motor will be out of phase. not good. dont drive it like that.
if you do it yourself, dont forget to remove the washer on the big bolt Michael talked about. if not removed, the damper does not like to come off. there are 3 or 4 bolts that hold the balancer on also, as i recall.
try doing an internet search for balancers, or go to strokermotors.com, etc and look up the balancer and see if it looks like what you are lookin at. might help. good luck.