flywheel ring gear??

the ring gear is what the starter engages when you start the car. :)

on some cars you can simply have a new gear pressed on an old flywheel.
 
Look at the balancer with the engine stopped. Is there any of the elastomer (rubber) squeezing out between the inner and outer halfs of the balancer? With the engine idling, does the balancer appear to be wobbling? Those are also signs of the balancer's demise. You can really damage things if it's bad and you don't replace it soon. If you end up having to replace it, you'll need a balancer puller to remove it. AutoZone will loan you one for a refundable deposit.