I'm in the same situation.  I have an SC200 currently sitting on my desk with a bad BNC connector.  I've torn into it enough to realize that replacing the connector isn't going to be just a de-solder and re-solder affair.  It served me well for about 10 years, but with more and more users going to trunking and/or digital radio systems, its usefulness is waning.  It'd still be good for Aircraft scanning, as well as any areas that still have a lot of analog conventional systems to listen to, but I'm on the fence as to whether it's even worth the $50 that Uniden would charge to repair it.
If the only thing keeping you from using it is the bad battery though, then definitely replace the battery.  I've replaced the pack in mine twice since I bought it.  I think they cost me between $10 and $15 or so each time.
If you still don't want it, you can always throw it on eBay for $10-20 and see who bites.  Or if you want to give it away, I'd sure take it for parts.  Might be the thing that finally motivates me to replace the BNC on mine.